Electricity price modeling with stochastic time change
International Nuclear Information System (INIS)
Borovkova, Svetlana; Schmeck, Maren Diane
2017-01-01
In this paper, we develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. This technique allows us to incorporate the characteristic features of electricity prices (such as seasonal volatility, time varying mean reversion and seasonally occurring price spikes) into the model in an elegant and economically justifiable way. The stochastic time change introduces stochastic as well as deterministic (e.g., seasonal) features in the price process' volatility and in the jump component. We specify the base process as a mean reverting jump diffusion and the time change as an absolutely continuous stochastic process with seasonal component. The activity rate of the stochastic time change can be related to the factors that influence supply and demand. Here we use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change, and show that this choice leads to realistic price paths. We derive properties of the resulting price process and develop the model calibration procedure. We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths by Monte Carlo simulations. We show that the simulated price process matches the distributional characteristics of the observed electricity prices in periods of both high and low demand. - Highlights: • We develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. • We incorporate the characteristic features of electricity prices, such as seasonal volatility and spikes into the model. • We use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change • We derive properties of the resulting price process and develop the model calibration procedure. • We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths.
Stochastic models for time series
Doukhan, Paul
2018-01-01
This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit ...
Computer Aided Continuous Time Stochastic Process Modelling
DEFF Research Database (Denmark)
Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay
2001-01-01
A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...
On the small-time behavior of stochastic logistic models
Directory of Open Access Journals (Sweden)
Dung Tien Nguyen
2017-09-01
Full Text Available In this paper we investigate the small-time behaviors of the solution to a stochastic logistic model. The obtained results allow us to estimate the number of individuals in the population and can be used to study stochastic prey-predator systems.
Time-Weighted Balanced Stochastic Model Reduction
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2011-01-01
A new relative error model reduction technique for linear time invariant (LTI) systems is proposed in this paper. Both continuous and discrete time systems can be reduced within this framework. The proposed model reduction method is mainly based upon time-weighted balanced truncation and a recently...
A stochastic surplus production model in continuous time
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte
2017-01-01
surplus production model in continuous time (SPiCT), which in addition to stock dynamics also models the dynamics of the fisheries. This enables error in the catch process to be reflected in the uncertainty of estimated model parameters and management quantities. Benefits of the continuous-time state......Surplus production modelling has a long history as a method for managing data-limited fish stocks. Recent advancements have cast surplus production models as state-space models that separate random variability of stock dynamics from error in observed indices of biomass. We present a stochastic......-space model formulation include the ability to provide estimates of exploitable biomass and fishing mortality at any point in time from data sampled at arbitrary and possibly irregular intervals. We show in a simulation that the ability to analyse subannual data can increase the effective sample size...
Investment timing decisions in a stochastic duopoly model
Energy Technology Data Exchange (ETDEWEB)
Marseguerra, Giovanni [Istituto di Econometria e CRANEC, Universita Cattolica del Sacro Cuore di Milan (Italy)]. E-mail: giovanni.marseguerra@unicatt.it; Cortelezzi, Flavia [Dipartimento di Diritto ed Economia delle Persone e delle Imprese, Universita dell' Insubria (Italy)]. E-mail: flavia.cortelezzi@uninsubria.it; Dominioni, Armando [CORE-Catholique de Louvain la Neuve (Belgium)]. E-mail: dominioni@core.ucl.ac.be
2006-08-15
We investigate the role of strategic considerations on the optimal timing of investment when firms compete for a new market (e.g., the provision of an innovative product) under demand uncertainty. Within a continuous time model of stochastic oligopoly, we show that strategic considerations are likely to be of limited impact when the new product is radically innovative whilst the fear of a rival's entry may deeply affect firms' decisions whenever innovation is to some extent limited. The welfare analysis shows surprisingly that the desirability of the different market structures considered does not depend on the fixed entry cost.
Investment timing decisions in a stochastic duopoly model
International Nuclear Information System (INIS)
Marseguerra, Giovanni; Cortelezzi, Flavia; Dominioni, Armando
2006-01-01
We investigate the role of strategic considerations on the optimal timing of investment when firms compete for a new market (e.g., the provision of an innovative product) under demand uncertainty. Within a continuous time model of stochastic oligopoly, we show that strategic considerations are likely to be of limited impact when the new product is radically innovative whilst the fear of a rival's entry may deeply affect firms' decisions whenever innovation is to some extent limited. The welfare analysis shows surprisingly that the desirability of the different market structures considered does not depend on the fixed entry cost
TIME-DEPENDENT STOCHASTIC ACCELERATION MODEL FOR FERMI BUBBLES
Energy Technology Data Exchange (ETDEWEB)
Sasaki, Kento; Asano, Katsuaki; Terasawa, Toshio, E-mail: kentos@icrr.u-tokyo.ac.jp, E-mail: asanok@icrr.u-tokyo.ac.jp, E-mail: terasawa@icrr.u-tokyo.ac.jp [Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582 (Japan)
2015-12-01
We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin–Helmholtz, Rayleigh–Taylor, or Richtmyer–Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is different from those for a steady solution. We also show that the contribution of electrons that escaped from the acceleration regions significantly softens the photon spectrum. The photon spectrum and surface brightness profile are reproduced by our models. If the escape efficiency is very high, the radio flux from the escaped low-energy electrons can be comparable to that of the WMAP haze. We also demonstrate hadronic models with the stochastic acceleration, but they are unlikely in the viewpoint of the energy budget.
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Doubly stochastic Poisson process models for precipitation at fine time-scales
Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao
2012-09-01
This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.
Modeling stochastic lead times in multi-echelon systems
Diks, E.B.; Heijden, van der M.C.
1996-01-01
In many multi-echelon inventory systems the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process which generates such lead times is usually not
Modeling stochastic lead times in multi-echelon systems
Diks, E.B.; van der Heijden, M.C.
1997-01-01
In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well
Optimal investment models with stochastic volatility: the time ...
African Journals Online (AJOL)
Therefore, a transform is primordial to express the value function in terms of a semilinear PDE with quadratic growth on the derivative term. Some proofs for the existence of smooth solution to this equation have been provided for this equation by Pham [11]. In that paper they illustrated some common stochastic volatility ...
Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator
González Ochoa, Héctor O.; Perales, Gualberto Solís; Epstein, Irving R.; Femat, Ricardo
2018-05-01
We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.
A stochastic space-time model for intermittent precipitation occurrences
Sun, Ying; Stein, Michael L.
2016-01-01
Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time t random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.
A stochastic space-time model for intermittent precipitation occurrences
Sun, Ying
2016-01-28
Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time t random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.
Stochastic modeling of hourly rainfall times series in Campania (Italy)
Giorgio, M.; Greco, R.
2009-04-01
Occurrence of flowslides and floods in small catchments is uneasy to predict, since it is affected by a number of variables, such as mechanical and hydraulic soil properties, slope morphology, vegetation coverage, rainfall spatial and temporal variability. Consequently, landslide risk assessment procedures and early warning systems still rely on simple empirical models based on correlation between recorded rainfall data and observed landslides and/or river discharges. Effectiveness of such systems could be improved by reliable quantitative rainfall prediction, which can allow gaining larger lead-times. Analysis of on-site recorded rainfall height time series represents the most effective approach for a reliable prediction of local temporal evolution of rainfall. Hydrological time series analysis is a widely studied field in hydrology, often carried out by means of autoregressive models, such as AR, ARMA, ARX, ARMAX (e.g. Salas [1992]). Such models gave the best results when applied to the analysis of autocorrelated hydrological time series, like river flow or level time series. Conversely, they are not able to model the behaviour of intermittent time series, like point rainfall height series usually are, especially when recorded with short sampling time intervals. More useful for this issue are the so-called DRIP (Disaggregated Rectangular Intensity Pulse) and NSRP (Neymann-Scott Rectangular Pulse) model [Heneker et al., 2001; Cowpertwait et al., 2002], usually adopted to generate synthetic point rainfall series. In this paper, the DRIP model approach is adopted, in which the sequence of rain storms and dry intervals constituting the structure of rainfall time series is modeled as an alternating renewal process. Final aim of the study is to provide a useful tool to implement an early warning system for hydrogeological risk management. Model calibration has been carried out with hourly rainfall hieght data provided by the rain gauges of Campania Region civil
Directory of Open Access Journals (Sweden)
Noble Mark
2006-05-01
Full Text Available Abstract Background The purpose of this paper is two-fold. The first objective is to validate the assumptions behind a stochastic model developed earlier by these authors to describe oligodendrocyte generation in cell culture. The second is to generate time-lapse data that may help biomathematicians to build stochastic models of cell proliferation and differentiation under other experimental scenarios. Results Using time-lapse video recording it is possible to follow the individual evolutions of different cells within each clone. This experimental technique is very laborious and cannot replace model-based quantitative inference from clonal data. However, it is unrivalled in validating the structure of a stochastic model intended to describe cell proliferation and differentiation at the clonal level. In this paper, such data are reported and analyzed for oligodendrocyte precursor cells cultured in vitro. Conclusion The results strongly support the validity of the most basic assumptions underpinning the previously proposed model of oligodendrocyte development in cell culture. However, there are some discrepancies; the most important is that the contribution of progenitor cell death to cell kinetics in this experimental system has been underestimated.
A fire management simulation model using stochastic arrival times
Eric L. Smith
1987-01-01
Fire management simulation models are used to predict the impact of changes in the fire management program on fire outcomes. As with all models, the goal is to abstract reality without seriously distorting relationships between variables of interest. One important variable of fire organization performance is the length of time it takes to get suppression units to the...
Stochastic time-dependent vehicle routing problem: Mathematical models and ant colony algorithm
Directory of Open Access Journals (Sweden)
Zhengyu Duan
2015-11-01
Full Text Available This article addresses the stochastic time-dependent vehicle routing problem. Two mathematical models named robust optimal schedule time model and minimum expected schedule time model are proposed for stochastic time-dependent vehicle routing problem, which can guarantee delivery within the time windows of customers. The robust optimal schedule time model only requires the variation range of link travel time, which can be conveniently derived from historical traffic data. In addition, the robust optimal schedule time model based on robust optimization method can be converted into a time-dependent vehicle routing problem. Moreover, an ant colony optimization algorithm is designed to solve stochastic time-dependent vehicle routing problem. As the improvements in initial solution and transition probability, ant colony optimization algorithm has a good performance in convergence. Through computational instances and Monte Carlo simulation tests, robust optimal schedule time model is proved to be better than minimum expected schedule time model in computational efficiency and coping with the travel time fluctuations. Therefore, robust optimal schedule time model is applicable in real road network.
Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2012-01-01
A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...... by using the concept and properties of the reciprocal systems. The results are further illustrated by two practical numerical examples: a model of CD player and a model of the atmospheric storm track....
Keren, Baruch; Pliskin, Joseph S
2011-12-01
The optimal timing for performing radical medical procedures as joint (e.g., hip) replacement must be seriously considered. In this paper we show that under deterministic assumptions the optimal timing for joint replacement is a solution of a mathematical programming problem, and under stochastic assumptions the optimal timing can be formulated as a stochastic programming problem. We formulate deterministic and stochastic models that can serve as decision support tools. The results show that the benefit from joint replacement surgery is heavily dependent on timing. Moreover, for a special case where the patient's remaining life is normally distributed along with a normally distributed survival of the new joint, the expected benefit function from surgery is completely solved. This enables practitioners to draw the expected benefit graph, to find the optimal timing, to evaluate the benefit for each patient, to set priorities among patients and to decide if joint replacement should be performed and when.
Assessing and accounting for time heterogeneity in stochastic actor oriented models
Lospinoso, Joshua A.; Schweinberger, Michael; Snijders, Tom A. B.; Ripley, Ruth M.
This paper explores time heterogeneity in stochastic actor oriented models (SAOM) proposed by Snijders (Sociological methodology. Blackwell, Boston, pp 361-395, 2001) which are meant to study the evolution of networks. SAOMs model social networks as directed graphs with nodes representing people,
The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates
Directory of Open Access Journals (Sweden)
Yilun Shang
2013-01-01
Full Text Available We investigate a variant of the stochastic logistic model that allows individual variation and time-dependent infection and recovery rates. The model is described as a heterogeneous density dependent Markov chain. We show that the process can be approximated by a deterministic process defined by an integral equation as the population size grows.
Capasso, Vincenzo
2015-01-01
This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics, and epidemics * Agent-based models New to the Third Edition: * Infinitely divisible distributions * Random measures * Levy processes * Fractional Brownian motion * Ergodic theory * Karhunen-Loeve expansion * Additional applications * Additional exercises * Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Editio...
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
International Nuclear Information System (INIS)
Olsson, Magnus; Perninge, Magnus; Soeder, Lennart
2010-01-01
The inclusion of wind power into power systems has a significant impact on the demand for real-time balancing power due to the stochastic nature of wind power production. The overall aim of this paper is to present probabilistic models of the impact of large-scale integration of wind power on the continuous demand in MW for real-time balancing power. This is important not only for system operators, but also for producers and consumers since they in most systems through various market solutions provide balancing power. Since there can occur situations where the wind power variations cancel out other types of deviations in the system, models on an hourly basis are not sufficient. Therefore the developed model is in continuous time and is based on stochastic differential equations (SDE). The model can be used within an analytical framework or in Monte Carlo simulations. (author)
Reconstructing the hidden states in time course data of stochastic models.
Zimmer, Christoph
2015-11-01
Parameter estimation is central for analyzing models in Systems Biology. The relevance of stochastic modeling in the field is increasing. Therefore, the need for tailored parameter estimation techniques is increasing as well. Challenges for parameter estimation are partial observability, measurement noise, and the computational complexity arising from the dimension of the parameter space. This article extends the multiple shooting for stochastic systems' method, developed for inference in intrinsic stochastic systems. The treatment of extrinsic noise and the estimation of the unobserved states is improved, by taking into account the correlation between unobserved and observed species. This article demonstrates the power of the method on different scenarios of a Lotka-Volterra model, including cases in which the prey population dies out or explodes, and a Calcium oscillation system. Besides showing how the new extension improves the accuracy of the parameter estimates, this article analyzes the accuracy of the state estimates. In contrast to previous approaches, the new approach is well able to estimate states and parameters for all the scenarios. As it does not need stochastic simulations, it is of the same order of speed as conventional least squares parameter estimation methods with respect to computational time. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
DEFF Research Database (Denmark)
Foddai, Alessandro; Enøe, Claes; Krogh, Kaspar
2014-01-01
A stochastic simulation model was developed to estimate the time from introduction ofBovine Viral Diarrhea Virus (BVDV) in a herd to detection of antibodies in bulk tank milk(BTM) samples using three ELISAs. We assumed that antibodies could be detected, after afixed threshold prevalence of seroco......A stochastic simulation model was developed to estimate the time from introduction ofBovine Viral Diarrhea Virus (BVDV) in a herd to detection of antibodies in bulk tank milk(BTM) samples using three ELISAs. We assumed that antibodies could be detected, after afixed threshold prevalence......, which was the most efficient ELISA, could detect antibodiesin the BTM of a large herd 280 days (95% prediction interval: 218; 568) after a transientlyinfected (TI) milking cow has been introduced into the herd. The estimated time to detectionafter introduction of one PI calf was 111 days (44; 605...
Stochastic models for structured populations scaling limits and long time behavior
Meleard, Sylvie
2015-01-01
In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured P...
Directory of Open Access Journals (Sweden)
Ryota Mori
2015-01-01
Full Text Available Airport congestion, in particular congestion of departure aircraft, has already been discussed by other researches. Most solutions, though, fail to account for uncertainties. Since it is difficult to remove uncertainties of the operations in the real world, a strategy should be developed assuming such uncertainties exist. Therefore, this research develops a fast-time stochastic simulation model used to validate various methods in order to decrease airport congestion level under existing uncertainties. The surface movement data is analyzed first, and the uncertainty level is obtained. Next, based on the result of data analysis, the stochastic simulation model is developed. The model is validated statistically and the characteristics of airport operation under existing uncertainties are investigated.
Anderson, David F; Yuan, Chaojie
2018-04-18
A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an exceptionally low variance between the generated paths. This coupling will be useful in the numerical computation of parametric sensitivities and the fast estimation of expectations via multilevel Monte Carlo methods. We provide the requisite estimators in both cases.
Moeeni, Hamid; Bonakdari, Hossein; Fatemi, Seyed Ehsan
2017-04-01
Because time series stationarization has a key role in stochastic modeling results, three methods are analyzed in this study. The methods are seasonal differencing, seasonal standardization and spectral analysis to eliminate the periodic effect on time series stationarity. First, six time series including 4 streamflow series and 2 water temperature series are stationarized. The stochastic term for these series obtained with ARIMA is subsequently modeled. For the analysis, 9228 models are introduced. It is observed that seasonal standardization and spectral analysis eliminate the periodic term completely, while seasonal differencing maintains seasonal correlation structures. The obtained results indicate that all three methods present acceptable performance overall. However, model accuracy in monthly streamflow prediction is higher with seasonal differencing than with the other two methods. Another advantage of seasonal differencing over the other methods is that the monthly streamflow is never estimated as negative. Standardization is the best method for predicting monthly water temperature although it is quite similar to seasonal differencing, while spectral analysis performed the weakest in all cases. It is concluded that for each monthly seasonal series, seasonal differencing is the best stationarization method in terms of periodic effect elimination. Moreover, the monthly water temperature is predicted with more accuracy than monthly streamflow. The criteria of the average stochastic term divided by the amplitude of the periodic term obtained for monthly streamflow and monthly water temperature were 0.19 and 0.30, 0.21 and 0.13, and 0.07 and 0.04 respectively. As a result, the periodic term is more dominant than the stochastic term for water temperature in the monthly water temperature series compared to streamflow series.
The Long Time Behavior of a Stochastic Logistic Model with Infinite Delay and Impulsive Perturbation
Lu, Chun; Wu, Kaining
2016-01-01
This paper considers a stochastic logistic model with infinite delay and impulsive perturbation. Firstly, with the space $C_{g}$ as phase space, the definition of solution to a stochastic functional differential equation with infinite delay and impulsive perturbation is established. According to this definition, we show that our model has an unique global positive solution. Then we establish the sufficient and necessary conditions for extinction and stochastic permanence of the...
Stochastic volatility of volatility in continuous time
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Veraart, Almut
This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility...... of volatility can be defined both non-parametrically, where we link it to the quadratic variation of the stochastic variance process, and parametrically, where we propose two new SV models which allow for stochastic volatility of volatility. In addition, we show that volatility of volatility can be estimated...
A stochastic fractional dynamics model of space-time variability of rain
Kundu, Prasun K.; Travis, James E.
2013-09-01
varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
Zhang, Wei; Wang, Jun
2017-09-01
In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.
ARIMA-Based Time Series Model of Stochastic Wind Power Generation
DEFF Research Database (Denmark)
Chen, Peiyuan; Pedersen, Troels; Bak-Jensen, Birgitte
2010-01-01
This paper proposes a stochastic wind power model based on an autoregressive integrated moving average (ARIMA) process. The model takes into account the nonstationarity and physical limits of stochastic wind power generation. The model is constructed based on wind power measurement of one year from...... the Nysted offshore wind farm in Denmark. The proposed limited-ARIMA (LARIMA) model introduces a limiter and characterizes the stochastic wind power generation by mean level, temporal correlation and driving noise. The model is validated against the measurement in terms of temporal correlation...... and probability distribution. The LARIMA model outperforms a first-order transition matrix based discrete Markov model in terms of temporal correlation, probability distribution and model parameter number. The proposed LARIMA model is further extended to include the monthly variation of the stochastic wind power...
Extinction time of a stochastic predator-prey model by the generalized cell mapping method
Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao
2018-03-01
The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.
Supply Chain Model with Stochastic Lead Time, Trade-Credit Financing, and Transportation Discounts
Directory of Open Access Journals (Sweden)
Sung Jun Kim
2017-01-01
Full Text Available This model extends a two-echelon supply chain model by considering the trade-credit policy, transportations discount to make a coordination mechanism between transportation discounts, trade-credit financing, number of shipments, quality improvement of products, and reduced setup cost in such a way that the total cost of the whole system can be reduced, where the supplier offers trade-credit-period to the buyer. For buyer, the backorder rate is considered as variable. There are two investments to reduce setup cost and to improve quality of products. The model assumes lead time-dependent backorder rate, where the lead time is stochastic in nature. By using the trade-credit policy, the model gives how the credit-period would be determined to achieve the win-win outcome. An iterative algorithm is designed to obtain the global optimum results. Numerical example and sensitivity analysis are given to illustrate the model.
Transport properties of stochastic Lorentz models
Beijeren, H. van
Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed
Energy Technology Data Exchange (ETDEWEB)
Dong, Jing [ORNL; Mahmassani, Hani S. [Northwestern University, Evanston
2011-01-01
This paper proposes a methodology to produce random flow breakdown endogenously in a mesoscopic operational model, by capturing breakdown probability and duration. Based on previous research findings that probability of flow breakdown can be represented as a function of flow rate and the duration can be characterized by a hazard model. By generating random flow breakdown at various levels and capturing the traffic characteristics at the onset of the breakdown, the stochastic network simulation model provides a tool for evaluating travel time variability. The proposed model can be used for (1) providing reliability related traveler information; (2) designing ITS (intelligent transportation systems) strategies to improve reliability; and (3) evaluating reliability-related performance measures of the system.
Stochastic modeling for time series InSAR: with emphasis on atmospheric effects
Cao, Yunmeng; Li, Zhiwei; Wei, Jianchao; Hu, Jun; Duan, Meng; Feng, Guangcai
2018-02-01
Despite the many applications of time series interferometric synthetic aperture radar (TS-InSAR) techniques in geophysical problems, error analysis and assessment have been largely overlooked. Tropospheric propagation error is still the dominant error source of InSAR observations. However, the spatiotemporal variation of atmospheric effects is seldom considered in the present standard TS-InSAR techniques, such as persistent scatterer interferometry and small baseline subset interferometry. The failure to consider the stochastic properties of atmospheric effects not only affects the accuracy of the estimators, but also makes it difficult to assess the uncertainty of the final geophysical results. To address this issue, this paper proposes a network-based variance-covariance estimation method to model the spatiotemporal variation of tropospheric signals, and to estimate the temporal variance-covariance matrix of TS-InSAR observations. The constructed stochastic model is then incorporated into the TS-InSAR estimators both for parameters (e.g., deformation velocity, topography residual) estimation and uncertainty assessment. It is an incremental and positive improvement to the traditional weighted least squares methods to solve the multitemporal InSAR time series. The performance of the proposed method is validated by using both simulated and real datasets.
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Stochastic models in the DORIS position time series: estimates for IDS contribution to ITRF2014
Klos, Anna; Bogusz, Janusz; Moreaux, Guilhem
2017-11-01
This paper focuses on the investigation of the deterministic and stochastic parts of the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) weekly time series aligned to the newest release of ITRF2014. A set of 90 stations was divided into three groups depending on when the data were collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations and a stochastic part, all being estimated with maximum likelihood estimation. We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations. The quality of the most recent data has significantly improved. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. Among several tested models, the power-law process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from an autoregressive process to pure power-law noise with few stations characterised by a positive spectral index. For the latest observations, the medians of the velocity errors were equal to 0.3, 0.3 and 0.4 mm/year, respectively, for the North, East and Up components. In the best cases, a velocity uncertainty of DORIS sites of 0.1 mm/year is achievable when the appropriate coloured noise model is taken into consideration.
Chen, Yonghong; Bressler, Steven L.; Knuth, Kevin H.; Truccolo, Wilson A.; Ding, Mingzhou
2006-06-01
In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis. After subtracting out the event-related signal from recorded single trial time series, the residual ongoing activity is treated as a piecewise stationary stochastic process and analyzed by an adaptive multivariate autoregressive modeling strategy which yields power, coherence, and Granger causality spectra. Results from applying these methods to local field potential recordings from monkeys performing cognitive tasks are presented.
An approach to the drone fleet survivability assessment based on a stochastic continues-time model
Kharchenko, Vyacheslav; Fesenko, Herman; Doukas, Nikos
2017-09-01
An approach and the algorithm to the drone fleet survivability assessment based on a stochastic continues-time model are proposed. The input data are the number of the drones, the drone fleet redundancy coefficient, the drone stability and restoration rate, the limit deviation from the norms of the drone fleet recovery, the drone fleet operational availability coefficient, the probability of the drone failure-free operation, time needed for performing the required tasks by the drone fleet. The ways for improving the recoverable drone fleet survivability taking into account amazing factors of system accident are suggested. Dependencies of the drone fleet survivability rate both on the drone stability and the number of the drones are analysed.
A stochastic model of radiation carcinogenesis: Latent time distributions and their properties
International Nuclear Information System (INIS)
Klebanov, L.V.; Yakovlev, A.Yu.; Rachev, S.T.
1993-01-01
A stochastic model of radiation carcinogenesis is proposed that has much in common with the ideas suggested by M. Pike as early as 1966. The model allows one to obtain a parametric family of substochastic-type distributions for the time of tumor latency that provides a description of the rate of tumor development and the number of affected individuals. With this model it is possible to interpret data on tumor incidence in terms of promotion and progression processes. The basic model is developed for a prolonged irradiation at a constant dose rate and includes short-term irradiation as a special case. A limiting form of the latent time distribution for short-term irradiation at high doses is obtained. This distribution arises in the extreme value theory within the random minima framework. An estimate for the rate of convergence to a limiting distributions is given. Based on the proposed latent time distributions, long-term predictions of carcinogenic risk do not call for information about irradiation dose. As shown by computer simulation studies and real data analysis, the parametric estimation of carcinogenic risk appears to be robust to the loss of statistical information caused by the right-hand censoring of time-to-tumor observations. It seems likely that this property, although revealed by means of a purely empirical procedure, may be useful in selecting a model for the practical purpose of risk prediction. 44 refs., 3 figs., 1 tab
A stochastic HMM-based forecasting model for fuzzy time series.
Li, Sheng-Tun; Cheng, Yi-Chung
2010-10-01
Recently, fuzzy time series have attracted more academic attention than traditional time series due to their capability of dealing with the uncertainty and vagueness inherent in the data collected. The formulation of fuzzy relations is one of the key issues affecting forecasting results. Most of the present works adopt IF-THEN rules for relationship representation, which leads to higher computational overhead and rule redundancy. Sullivan and Woodall proposed a Markov-based formulation and a forecasting model to reduce computational overhead; however, its applicability is limited to handling one-factor problems. In this paper, we propose a novel forecasting model based on the hidden Markov model by enhancing Sullivan and Woodall's work to allow handling of two-factor forecasting problems. Moreover, in order to make the nature of conjecture and randomness of forecasting more realistic, the Monte Carlo method is adopted to estimate the outcome. To test the effectiveness of the resulting stochastic model, we conduct two experiments and compare the results with those from other models. The first experiment consists of forecasting the daily average temperature and cloud density in Taipei, Taiwan, and the second experiment is based on the Taiwan Weighted Stock Index by forecasting the exchange rate of the New Taiwan dollar against the U.S. dollar. In addition to improving forecasting accuracy, the proposed model adheres to the central limit theorem, and thus, the result statistically approximates to the real mean of the target value being forecast.
Stochastic integrated vendor–buyer model with unstable lead time and setup cost
Directory of Open Access Journals (Sweden)
Chandra K. Jaggi
2011-01-01
Full Text Available This paper presents a new vendor-buyer system where there are different objectives for both sides. The proposed method of this paper is different from the other previously published works since it considers different objectives for both sides. In this paper, the vendor’s emphasis is on the crashing of the setup cost, which not only helps him compete in the market but also provides better services to his customers; and the buyer’s aim is to reduce the lead time, which not only facilitates the buyer to fulfill the customers’ demand on time but also enables him to earn a good reputation in the market or vice versa. In the light of the above stated facts, an integrated vendor-buyer stochastic inventory model is also developed. The propsed model considers two cases for demand during lead time: Case (i Complete demand information, Case (ii Partial demand information. The proposed model jointly optimizes the buyer’s ordered quantity and lead time along with vendor’s setup cost and the number of shipments. The results are demonstrated with the help of numerical examples.
An Innovative Real-time Environment for Unified Deterministic and Stochastic Groundwater Modeling
Li, S.; Liu, Q.
2003-12-01
Despite an exponential growth of computational capability over the last two decades-one that has allowed computational science and engineering to become a unique, powerful tool for scientific discovery-the extreme cost of groundwater modeling continues to limit its use. This occurs primarily because the modeling paradigm that has been employed for decades limits our ability to take full advantage of recent developments in computer, communication, graphic, and visualization technologies. In this presentation we introduce an innovative and sophisticated computational environment for groundwater modeling that promises to eliminate the current bottleneck and greatly expand the utility of computational tools for scientific discovery related to groundwater. Based on a set of efficient and robust computational algorithms, the new software system, called Interactive Groundwater (IGW), allows simulating complex flow and transport in aquifers subject to both systematic and "randomly" varying stresses and geological and chemical heterogeneity. Adopting a new paradigm, IGW eliminates a major bottleneck inherent in the traditional fragmented modeling technologies and enables real-time modeling, real-time visualization, real-time analysis, and real-time presentation. IGW functions as a "numerical laboratory" in which a researcher can freely explore in real-time: creating visually an aquifer of desired configurations, interactively imposing desired stresses, and then immediately investigating and visualizing the geology and the processes of flow and contaminant transport and transformation. A modeler can pause to edit at any time and interact on-line with any aspects (e.g., conceptual and numerical representation, boundary conditions, model solvers, and ways of visualization and analysis) of the integrated modeling process; he/she can initiate or stop, whenever needed, particle tracking, plume modeling, subscale modeling, cross-sectional modeling, stochastic modeling, monitoring
GCSRL - A Logic for Stochastic Reward Models with Timed and Untimed Behaviour
Kuntz, Matthias; Haverkort, Boudewijn R.; Cloth, L.
In this paper we define the logic GCSRL (generalised continuous stochastic reward logic) that provides means to reason about systems that have states which sojourn times are either greater zero, in which case this sojourn time is exponentially distributed (tangible states), or zero (vanishing
Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality
Saldi, Naci; Yüksel, Serdar
2018-01-01
In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original mo...
Space-time-modulated stochastic processes
Giona, Massimiliano
2017-10-01
Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...
Stochastic modeling and analysis of telecoms networks
Decreusefond, Laurent
2012-01-01
This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an
Bakhtavar, E.; Abdollahisharif, J.; Aminzadeh, A.
2017-01-01
This research introduces a stochastic mathematical model that uses open pit long-term production planning on an integrated open pit and underground block model to determine the optimal time for transition from open pit to underground mining. In the model, ore grade is considered a random parameter in objective function and ore grade blending constraints. The objective function is modelled as the maximization of net present value in the mode of non-simultaneous combined open pit and undergroun...
Stochastic models: theory and simulation.
Energy Technology Data Exchange (ETDEWEB)
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
D'Onofrio, Giuseppe; Pirozzi, Enrica
2017-05-01
We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.
Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models
Zhang, Xin
2016-01-01
Asymptotic behavior of implied volatility is of our interest in this dissertation. For extreme strike, we consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the asset price density for large or smal...
Czech Academy of Sciences Publication Activity Database
Baruník, Jozef; Kukačka, Jiří
2015-01-01
Roč. 15, č. 6 (2015), s. 959-973 ISSN 1469-7688 R&D Projects: GA ČR GA402/09/0965; GA ČR GA13-32263S EU Projects: European Commission 612955 - FINMAP Institutional support: RVO:67985556 Keywords : Stochastic cusp catastrophe model * Realized volatility * Bifurcations * Stock market crash Subject RIV: AH - Economics Impact factor: 0.794, year: 2015 http://library.utia.cas.cz/separaty/2014/E/barunik-0434202.pdf
Stochastic models of cell motility
DEFF Research Database (Denmark)
Gradinaru, Cristian
2012-01-01
Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...
Stochastic Modelling of Hydrologic Systems
DEFF Research Database (Denmark)
Jonsdottir, Harpa
2007-01-01
In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...... are described, as at the time of publication these methods represent new contribution to hydrology. The second part also contains additional description of software used and a brief introduction to stiff systems. The system in one of the papers is stiff....
Yan, S.; Lin, H. C.; Jiang, X. Y.
2012-04-01
In this study the authors employ network flow techniques to construct a systematic model that helps ready mixed concrete carriers effectively plan production and truck dispatching schedules under stochastic travel times. The model is formulated as a mixed integer network flow problem with side constraints. Problem decomposition and relaxation techniques, coupled with the CPLEX mathematical programming solver, are employed to develop an algorithm that is capable of efficiently solving the problems. A simulation-based evaluation method is also proposed to evaluate the model, coupled with a deterministic model, and the method currently used in actual operations. Finally, a case study is performed using real operating data from a Taiwan RMC firm. The test results show that the system operating cost obtained using the stochastic model is a significant improvement over that obtained using the deterministic model or the manual approach. Consequently, the model and the solution algorithm could be useful for actual operations.
Stochastic time scale for the Universe
International Nuclear Information System (INIS)
Szydlowski, M.; Golda, Z.
1986-01-01
An intrinsic time scale is naturally defined within stochastic gradient dynamical systems. It should be interpreted as a ''relaxation time'' to a local potential minimum after the system has been randomly perturbed. It is shown that for a flat Friedman-like cosmological model this time scale is of order of the age of the Universe. 7 refs. (author)
Stochasticity Modeling in Memristors
Naous, Rawan; Al-Shedivat, Maruan; Salama, Khaled N.
2015-01-01
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Stochasticity Modeling in Memristors
Naous, Rawan
2015-10-26
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Campo, M. A.; Lopez, J. J.; Rebole, J. P.
2012-04-01
This work was carried out in north of Spain. San Sebastian A meteorological station, where there are available precipitation records every ten minutes was selected. Precipitation data covers from October of 1927 to September of 1997. Pulse models describe the temporal process of rainfall as a succession of rainy cells, main storm, whose origins are distributed in time according to a Poisson process and a secondary process that generates a random number of cells of rain within each storm. Among different pulse models, the Bartlett-Lewis was used. On the other hand, alternative renewal processes and Markov chains describe the way in which the process will evolve in the future depending only on the current state. Therefore they are nor dependant on past events. Two basic processes are considered when describing the occurrence of rain: the alternation of wet and dry periods and temporal distribution of rainfall in each rain event, which determines the rainwater collected in each of the intervals that make up the rain. This allows the introduction of alternative renewal processes and Markov chains of three states, where interstorm time is given by either of the two dry states, short or long. Thus, the stochastic model of Markov chains tries to reproduce the basis of pulse models: the succession of storms, each one composed for a series of rain, separated by a short interval of time without theoretical complexity of these. In a first step, we analyzed all variables involved in the sequential process of the rain: rain event duration, event duration of non-rain, average rainfall intensity in rain events, and finally, temporal distribution of rainfall within the rain event. Additionally, for pulse Bartlett-Lewis model calibration, main descriptive statistics were calculated for each month, considering the process of seasonal rainfall in each month. In a second step, both models were calibrated. Finally, synthetic series were simulated with calibration parameters; series
Identifiability in stochastic models
1992-01-01
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P
2008-01-01
Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...
Stochastic-field cavitation model
International Nuclear Information System (INIS)
Dumond, J.; Magagnato, F.; Class, A.
2013-01-01
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-01
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Stochastic ontogenetic growth model
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
International Nuclear Information System (INIS)
Sharma, P.; Khare, M.
2000-01-01
Historical data of the time-series of carbon monoxide (CO) concentration was analysed using Box-Jenkins modelling approach. Univariate Linear Stochastic Models (ULSMs) were developed to examine the degree of prediction possible for situations where only a limited data set, restricted only to the past record of pollutant data are available. The developed models can be used to provide short-term, real-time forecast of extreme CO concentrations for an Air Quality Control Region (AQCR), comprising a major traffic intersection in a Central Business District of Delhi City, India. (author)
International Nuclear Information System (INIS)
Pham, Nhu Viet Ha
2011-02-01
To predict the space-time dependent behavior of a nuclear reactor, the conventional space-dependent kinetics equations are widely used for treating the spatial variables. However, the solutions of such deterministic space-dependent kinetics equations, which give only the mean values of the neutron population and the delayed neutron precursor concentrations, do not offer sufficient insight into the actual dynamic processes within a reactor, where the interacting populations vary randomly with space and time. It is also noted that at high power levels, the random behavior of a reactor is negligible but at low power levels, such as at start-up, random fluctuations in population dynamics can be significant. To mathematically describe the evolution of the state of a nuclear reactor using a set of stochastic kinetics equations, the forward stochastic model (FSM) in stochastic kinetics theory is devised through the concept of reactor transition probability and its probability generating function as the spatial domain of a reactor is partitioned into a number of space cells. Nevertheless, the FSM equations for the mean value of neutron and precursor distribution are deterministic-like. Furthermore, the numerical treatment of the FSM equations for the means, variances, and covariances is quite complicated and time-consuming. In the present study, a generalized stochastic model (called the stochastic space-dependent kinetics model or SSKM) based on the FSM and the Its stochastic differential equations was newly developed for the analysis of monoenergetic spacetime nuclear reactor kinetics in one dimension. First, the FSM equations for determining the mean values of neutron and delayed-neutron precursor populations were considered as the deterministic ones without taking into account their variances and covariances. Second, the system of interest was randomized again in the light of the Its stochastic differential equations in order to derive the SSKM. The proposed model
DEFF Research Database (Denmark)
A methodology is presented that combines modelling based on first principles and data based modelling into a modelling cycle that facilitates fast decision-making based on statistical methods. A strong feature of this methodology is that given a first principles model along with process data......, the corresponding modelling cycle model of the given system for a given purpose. A computer-aided tool, which integrates the elements of the modelling cycle, is also presented, and an example is given of modelling a fed-batch bioreactor....
Klos, A.; Bogusz, J.; Moreaux, G.
2017-12-01
This research focuses on the investigation of the deterministic and stochastic parts of the DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) weekly coordinate time series from the IDS contribution to the ITRF2014A set of 90 stations was divided into three groups depending on when the data was collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations (these three sum up to produce the Polynomial Trend Model) and a stochastic part, all being resolved with Maximum Likelihood Estimation (MLE). We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations, meaning that the most recent data are the most reliable ones. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. We examined five different noise models to be applied to the stochastic part of the DORIS time series: a pure white noise (WN), a pure power-law noise (PL), a combination of white and power-law noise (WNPL), an autoregressive process of first order (AR(1)) and a Generalized Gauss Markov model (GGM). From our study it arises that the PL process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from AR(1) to pure PL with few stations characterized by a positive spectral index.
Alternative Asymmetric Stochastic Volatility Models
M. Asai (Manabu); M.J. McAleer (Michael)
2010-01-01
textabstractThe stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is
Directory of Open Access Journals (Sweden)
Nishiura Hiroshi
2011-02-01
Full Text Available Abstract Background Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. Methods A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009 in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. Results The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Conclusions Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.
Directory of Open Access Journals (Sweden)
Mindaugas Snipas
2015-01-01
Full Text Available The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC of voltage gating of gap junction (GJ channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs, which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ∼20 times.
Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Bukauskas, Feliksas F.
2015-01-01
The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ∼20 times. PMID:25705700
Stochastic forward and inverse groundwater flow and solute transport modeling
Janssen, G.M.C.M.
2008-01-01
Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers
This thesis offers three new approaches that contribute
Milne, R K; Yeo, G F; Edeson, R O; Madsen, B W
1988-04-22
Stochastic models of ion channels have been based largely on Markov theory where individual states and transition rates must be specified, and sojourn-time densities for each state are constrained to be exponential. This study presents an approach based on random-sum methods and alternating-renewal theory, allowing individual states to be grouped into classes provided the successive sojourn times in a given class are independent and identically distributed. Under these conditions Markov models form a special case. The utility of the approach is illustrated by considering the effects of limited time resolution (modelled by using a discrete detection limit, xi) on the properties of observable events, with emphasis on the observed open-time (xi-open-time). The cumulants and Laplace transform for a xi-open-time are derived for a range of Markov and non-Markov models; several useful approximations to the xi-open-time density function are presented. Numerical studies show that the effects of limited time resolution can be extreme, and also highlight the relative importance of the various model parameters. The theory could form a basis for future inferential studies in which parameter estimation takes account of limited time resolution in single channel records. Appendixes include relevant results concerning random sums and a discussion of the role of exponential distributions in Markov models.
Stochastic modeling analysis and simulation
Nelson, Barry L
1995-01-01
A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis. Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, se
Modeling and analysis of stochastic systems
Kulkarni, Vidyadhar G
2011-01-01
Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi
Modelling, interpolation and stochastic simulation in space and time of global solar radiation
Bechini, L.; Ducco, G.; Donatelli, M.; Stein, A.
2000-01-01
Global solar radiation data used as daily inputs for most cropping systems and water budget models are frequently available from only a few weather stations and over short periods of time. To overcome this limitation, the Campbell–Donatelli model relates daily maximum and minimum air temperatures to
Modelling and application of stochastic processes
1986-01-01
The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...
Stochastic Subspace Modelling of Turbulence
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
2009-01-01
positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order......, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.......Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper...
Dynamics of a Stochastic Intraguild Predation Model
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Zejing Xing
2016-04-01
Full Text Available Intraguild predation (IGP is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition.
The influences of delay time on the stability of a market model with stochastic volatility
Li, Jiang-Cheng; Mei, Dong-Cheng
2013-02-01
The effects of the delay time on the stability of a market model are investigated, by using a modified Heston model with a cubic nonlinearity and cross-correlated noise sources. These results indicate that: (i) There is an optimal delay time τo which maximally enhances the stability of the stock price under strong demand elasticity of stock price, and maximally reduces the stability of the stock price under weak demand elasticity of stock price; (ii) The cross correlation coefficient of noises and the delay time play an opposite role on the stability for the case of the delay time τo. Moreover, the probability density function of the escape time of stock price returns, the probability density function of the returns and the correlation function of the returns are compared with other literatures.
Stochastic time series analysis of hydrology data for water resources
Sathish, S.; Khadar Babu, S. K.
2017-11-01
The prediction to current publication of stochastic time series analysis in hydrology and seasonal stage. The different statistical tests for predicting the hydrology time series on Thomas-Fiering model. The hydrology time series of flood flow have accept a great deal of consideration worldwide. The concentration of stochastic process areas of time series analysis method are expanding with develop concerns about seasonal periods and global warming. The recent trend by the researchers for testing seasonal periods in the hydrologic flowseries using stochastic process on Thomas-Fiering model. The present article proposed to predict the seasonal periods in hydrology using Thomas-Fiering model.
Stochastic Models of Polymer Systems
2016-01-01
Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the...ADDRESS. Princeton University PO Box 0036 87 Prospect Avenue - 2nd floor Princeton, NJ 08544 -2020 14-Mar-2014 ABSTRACT Number of Papers published in...peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Stochastic Models of Polymer Systems Report Title
Time-ordered product expansions for computational stochastic system biology
International Nuclear Information System (INIS)
Mjolsness, Eric
2013-01-01
The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie’s stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems. (paper)
A Stochastic Model of Space-Time Variability of Tropical Rainfall: I. Statistics of Spatial Averages
Kundu, Prasun K.; Bell, Thomas L.; Lau, William K. M. (Technical Monitor)
2002-01-01
Global maps of rainfall are of great importance in connection with modeling of the earth s climate. Comparison between the maps of rainfall predicted by computer-generated climate models with observation provides a sensitive test for these models. To make such a comparison, one typically needs the total precipitation amount over a large area, which could be hundreds of kilometers in size over extended periods of time of order days or months. This presents a difficult problem since rain varies greatly from place to place as well as in time. Remote sensing methods using ground radar or satellites detect rain over a large area by essentially taking a series of snapshots at infrequent intervals and indirectly deriving the average rain intensity within a collection of pixels , usually several kilometers in size. They measure area average of rain at a particular instant. Rain gauges, on the other hand, record rain accumulation continuously in time but only over a very small area tens of centimeters across, say, the size of a dinner plate. They measure only a time average at a single location. In making use of either method one needs to fill in the gaps in the observation - either the gaps in the area covered or the gaps in time of observation. This involves using statistical models to obtain information about the rain that is missed from what is actually detected. This paper investigates such a statistical model and validates it with rain data collected over the tropical Western Pacific from ship borne radars during TOGA COARE (Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment). The model incorporates a number of commonly observed features of rain. While rain varies rapidly with location and time, the variability diminishes when averaged over larger areas or longer periods of time. Moreover, rain is patchy in nature - at any instant on the average only a certain fraction of the observed pixels contain rain. The fraction of area covered by
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic differential equation model to Prendiville processes
International Nuclear Information System (INIS)
Granita; Bahar, Arifah
2015-01-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution
Model of observed stochastic balance between work and free time supporting the LQTAI definition
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2008-01-01
A balance differential equation between free time and money-producing work time on the national economy level is formulated in a previous paper in terms of two dimensionless quantities, the fraction of work time and the total productivity factor defined as the ratio of the Gross Domestic Product...... significant systematically balance influencing parameters on the macro economical level than those considered in the definition in the previous paper of the Life Quality Time Allocation Index....... to the total salary paid in return for work. Among the solutions there is one relation that compares surprisingly well with the relevant sequences of Danish data spanning from 1948 to 2003, and also with similar data from several other countries except for slightly different model parameter values. Statistical...
Big Data impacts on stochastic Forecast Models: Evidence from FX time series
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Sebastian Dietz
2013-12-01
Full Text Available With the rise of the Big Data paradigm new tasks for prediction models appeared. In addition to the volume problem of such data sets nonlinearity becomes important, as the more detailed data sets contain also more comprehensive information, e.g. about non regular seasonal or cyclical movements as well as jumps in time series. This essay compares two nonlinear methods for predicting a high frequency time series, the USD/Euro exchange rate. The first method investigated is Autoregressive Neural Network Processes (ARNN, a neural network based nonlinear extension of classical autoregressive process models from time series analysis (see Dietz 2011. Its advantage is its simple but scalable time series process model architecture, which is able to include all kinds of nonlinearities based on the universal approximation theorem of Hornik, Stinchcombe and White 1989 and the extensions of Hornik 1993. However, restrictions related to the numeric estimation procedures limit the flexibility of the model. The alternative is a Support Vector Machine Model (SVM, Vapnik 1995. The two methods compared have different approaches of error minimization (Empirical error minimization at the ARNN vs. structural error minimization at the SVM. Our new finding is, that time series data classified as “Big Data” need new methods for prediction. Estimation and prediction was performed using the statistical programming language R. Besides prediction results we will also discuss the impact of Big Data on data preparation and model validation steps. Normal 0 21 false false false DE X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Normale Tabelle"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";}
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Hamidreza Mostafaei
2013-01-01
Full Text Available In this study, it has been attempted to select the best continuous- time stochastic model, in order to describe and forecast the oil price of Russia, by information and statistics about oil price that has been available for oil price in the past. For this purpose, method of The Maximum Likelihood Estimation is implemented for estimation of the parameters of continuous-time stochastic processes. The result of unit root test with a structural break, reveals that time series of the crude oil price is a stationary series. The simulation of continuous-time stochastic processes and the mean square error between the simulated prices and the market ones shows that the Geometric Brownian Motion is the best model for the Russian crude oil price.
On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout
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Yingqi Zhang
2012-01-01
Full Text Available This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.
International Nuclear Information System (INIS)
Pisciella, P.; Vespucci, M.T.; Bertocchi, M.; Zigrino, S.
2016-01-01
We propose a multi-stage stochastic optimization model for the generation capacity expansion problem of a price-taker power producer. Uncertainties regarding the evolution of electricity prices and fuel costs play a major role in long term investment decisions, therefore the objective function represents a trade-off between expected profit and risk. The Conditional Value at Risk is the risk measure used and is defined by a nested formulation that guarantees time consistency in the multi-stage model. The proposed model allows one to determine a long term expansion plan which takes into account uncertainty, while the LCoE approach, currently used by decision makers, only allows one to determine which technology should be chosen for the next power plant to be built. A sensitivity analysis is performed with respect to the risk weighting factor and budget amount. - Highlights: • We propose a time consistent risk averse multi-stage model for capacity expansion. • We introduce a case study with uncertainty on electricity prices and fuel costs. • Increased budget moves the investment from gas towards renewables and then coal. • Increased risk aversion moves the investment from coal towards renewables. • Time inconsistency leads to a profit gap between planned and implemented policies.
Optimizing Real-Time Vaccine Allocation in a Stochastic SIR Model.
Directory of Open Access Journals (Sweden)
Chantal Nguyen
Full Text Available Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in delayed vaccine deployment, and the interaction between members of different cities facilitates a wide spatial spread of infection. Limited vaccine, time delays, and interaction (or coupling of cities lead to tradeoffs that impact the overall magnitude of the epidemic. These tradeoffs mandate investigation of optimal strategies that minimize the severity of the epidemic by prioritizing allocation of vaccine to specific subpopulations. We use an SIR model to describe the disease dynamics of an epidemic which breaks out in one city and spreads to another. We solve a master equation to determine the resulting probability distribution of the final epidemic size. We then identify tradeoffs between vaccine, time delay, and coupling, and we determine the optimal vaccination protocols resulting from these tradeoffs.
Stochastic Still Water Response Model
DEFF Research Database (Denmark)
Friis-Hansen, Peter; Ditlevsen, Ove Dalager
2002-01-01
In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is...... out that an important parameter of the stochastic cargo field model is the mean number of containers delivered by each customer.......In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...
Using stochastic space-time models to map extreme precipitation in southern Portugal
Directory of Open Access Journals (Sweden)
A. C. Costa
2008-07-01
Full Text Available The topographic characteristics and spatial climatic diversity are significant in the South of continental Portugal where the rainfall regime is typically Mediterranean. Direct sequential cosimulation is proposed for mapping an extreme precipitation index in southern Portugal using elevation as auxiliary information. The analysed index (R5D can be considered a flood indicator because it provides a measure of medium-term precipitation total. The methodology accounts for local data variability and incorporates space-time models that allow capturing long-term trends of extreme precipitation, and local changes in the relationship between elevation and extreme precipitation through time. Annual gridded datasets of the flood indicator are produced from 1940 to 1999 on 800 m×800 m grids by using the space-time relationship between elevation and the index. Uncertainty evaluations of the proposed scenarios are also produced for each year. The results indicate that the relationship between elevation and extreme precipitation varies locally and has decreased through time over the study region. In wetter years the flood indicator exhibits the highest values in mountainous regions of the South, while in drier years the spatial pattern of extreme precipitation has much less variability over the study region. The uncertainty of extreme precipitation estimates also varies in time and space, and in earlier decades is strongly dependent on the density of the monitoring stations network. The produced maps will be useful in regional and local studies related to climate change, desertification, land and water resources management, hydrological modelling, and flood mitigation planning.
Stochastic nature of series of waiting times
Anvari, Mehrnaz; Aghamohammadi, Cina; Dashti-Naserabadi, H.; Salehi, E.; Behjat, E.; Qorbani, M.; Khazaei Nezhad, M.; Zirak, M.; Hadjihosseini, Ali; Peinke, Joachim; Tabar, M. Reza Rahimi
2013-06-01
Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the “waiting times” series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2
Factors influencing lysis time stochasticity in bacteriophage λ
Directory of Open Access Journals (Sweden)
Dennehy John J
2011-08-01
Full Text Available Abstract Background Despite identical genotypes and seemingly uniform environments, stochastic gene expression and other dynamic intracellular processes can produce considerable phenotypic diversity within clonal microbes. One trait that provides a good model to explore the molecular basis of stochastic variation is the timing of host lysis by bacteriophage (phage. Results Individual lysis events of thermally-inducible λ lysogens were observed using a temperature-controlled perfusion chamber mounted on an inverted microscope. Both mean lysis time (MLT and its associated standard deviation (SD were estimated. Using the SD as a measure of lysis time stochasticity, we showed that lysogenic cells in controlled environments varied widely in lysis times, and that the level of lysis time stochasticity depended on allelic variation in the holin sequence, late promoter (pR' activity, and host growth rate. In general, the MLT was positively correlated with the SD. Both lower pR' activities and lower host growth rates resulted in larger SDs. Results from premature lysis, induced by adding KCN at different time points after lysogen induction, showed a negative correlation between the timing of KCN addition and lysis time stochasticity. Conclusions Taken together with results published by others, we conclude that a large fraction of λ lysis time stochasticity is the result of random events following the expression and diffusion of the holin protein. Consequently, factors influencing the timing of reaching critical holin concentrations in the cell membrane, such as holin production rate, strongly influence the mean lysis time and the lysis time stochasticity.
Weather Derivatives and Stochastic Modelling of Temperature
Directory of Open Access Journals (Sweden)
Fred Espen Benth
2011-01-01
Full Text Available We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.
Stochastic hyperfine interactions modeling library
Zacate, Matthew O.; Evenson, William E.
2011-04-01
interactions fluctuate at rates comparable to the time scale of a hyperfine method, there is a loss in signal coherence, and spectra are damped. The degree of damping can be used to determine fluctuation rates, provided that theoretical expressions for spectra can be derived for relevant physical models of the fluctuations. SHIML provides routines to help researchers quickly develop code to incorporate stochastic models of fluctuating hyperfine interactions in calculations of hyperfine spectra. Solution method: Calculations are based on the method for modeling stochastic hyperfine interactions for PAC by Winkler and Gerdau [5]. The method is extended to include other hyperfine methods following the work of Dattagupta [6]. The code provides routines for reading model information from text files, allowing researchers to develop new models quickly without the need to modify computer code for each new model to be considered. Restrictions: In the present version of the code, only methods that measure the hyperfine interaction on one probe spin state, such as PAC, μSR, and NMR, are supported. Running time: Varies
Stochastic Modelling Of The Repairable System
Directory of Open Access Journals (Sweden)
Andrzejczak Karol
2015-11-01
Full Text Available All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.
International Nuclear Information System (INIS)
Wickart, Marcel; Madlener, Reinhard
2007-01-01
In this paper we develop an economic model that explains the decision-making problem under uncertainty of an industrial firm that wants to invest in a process technology. More specifically, the decision is between making an irreversible investment in a combined heat-and-power production (cogeneration) system, or to invest in a conventional heat-only generation system (steam boiler) and to purchase all electricity from the grid. In our model we include the main economic and technical variables of the investment decision process. We also account for the risk and uncertainty inherent in volatile energy prices that can greatly affect the valuation of the investment project. The dynamic stochastic model presented allows us to simultaneously determine the optimal technology choice and investment timing. We apply the theoretical model and illustrate our main findings with a numerical example that is based on realistic cost values for industrial oil- or gas-fired cogeneration and heat-only generation in Switzerland. We also briefly discuss expected effects of a CO 2 tax on the investment decision
From complex to simple: interdisciplinary stochastic models
International Nuclear Information System (INIS)
Mazilu, D A; Zamora, G; Mazilu, I
2012-01-01
We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions for certain physical quantities, such as the time dependence of the length of the microtubules, and diffusion coefficients. The second one is a stochastic adsorption model with applications in surface deposition, epidemics and voter systems. We introduce the ‘empty interval method’ and show sample calculations for the time-dependent particle density. These models can serve as an introduction to the field of non-equilibrium statistical physics, and can also be used as a pedagogical tool to exemplify standard statistical physics concepts, such as random walks or the kinetic approach of the master equation. (paper)
Deperas-Standylo, Joanna; Gudowska-Nowak, Ewa; Ritter, Sylvia
2014-07-01
Cytogenetic data accumulated from the experiments with peripheral blood lymphocytes exposed to densely ionizing radiation clearly demonstrate that for particles with linear energy transfer (LET) >100 keV/ μm the derived relative biological effectiveness (RBE) will strongly depend on the time point chosen for the analysis. A reasonable prediction of radiation-induced chromosome damage and its distribution among cells can be achieved by exploiting Monte Carlo methodology along with the information about the radius of the penetrating ion-track and the LET of the ion beam. In order to examine the relationship between the track structure and the distribution of aberrations induced in human lymphocytes and to clarify the correlation between delays in the cell cycle progression and the aberration burden visible at the first post-irradiation mitosis, we have analyzed chromosome aberrations in lymphocytes exposed to Fe-ions with LET values of 335 keV/ μm and formulated a Monte Carlo model which reflects time-delay in mitosis of aberrant cells. Within the model the frequency distributions of aberrations among cells follow the pattern of local energy distribution and are well approximated by a time-dependent compound Poisson statistics. The cell-division cycle of undamaged and aberrant cells and chromosome aberrations are modelled as a renewal process represented by a random sum of (independent and identically distributed) random elements S N = ∑ N i=0 X i . Here N stands for the number of particle traversals of cell nucleus, each leading to a statistically independent formation of X i aberrations. The parameter N is itself a random variable and reflects the cell cycle delay of heavily damaged cells. The probability distribution of S N follows a general law for which the moment generating function satisfies the relation Φ S N = Φ N ( Φ X i ). Formulation of the Monte Carlo model which allows to predict expected fluxes of aberrant and non-aberrant cells has been based
International Nuclear Information System (INIS)
Calabrese, Pasquale; Hagendorf, Christian; Doussal, Pierre Le
2008-01-01
We study the time evolution of quantum one-dimensional gapless systems evolving from initial states with a domain wall. We generalize the path integral imaginary time approach that together with boundary conformal field theory allows us to derive the time and space dependence of general correlation functions. The latter are explicitly obtained for the Ising universality class, and the typical behavior of one- and two-point functions is derived for the general case. Possible connections with the stochastic Loewner evolution are discussed and explicit results for one-point time dependent averages are obtained for generic κ for boundary conditions corresponding to stochastic Loewner evolution. We use this set of results to predict the time evolution of the entanglement entropy and obtain the universal constant shift due to the presence of a domain wall in the initial state
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Modeling and analysis for determining optimal suppliers under stochastic lead times
DEFF Research Database (Denmark)
Abginehchi, Soheil; Farahani, Reza Zanjirani
2010-01-01
systems. The item acquisition lead times of suppliers are random variables. Backorder is allowed and shortage cost is charged based on not only per unit in shortage but also per time unit. Continuous review (s,Q) policy has been assumed. When the inventory level depletes to a reorder level, the total...... order is split among n suppliers. Since the suppliers have different characteristics, the quantity ordered to different suppliers may be different. The problem is to determine the reorder level and quantity ordered to each supplier so that the expected total cost per time unit, including ordering cost...
Stochastic Volatility and DSGE Models
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper argues that a specification of stochastic volatility commonly used to analyze the Great Moderation in DSGE models may not be appropriate, because the level of a process with this specification does not have conditional or unconditional moments. This is unfortunate because agents may...
International Nuclear Information System (INIS)
Lee, Youn Myoung
1995-02-01
As a newly approaching model, a stochastic model using continuous time Markov process for nuclide decay chain transport of arbitrary length in the fractured porous rock medium has been proposed, by which the need for solving a set of partial differential equations corresponding to various sets of side conditions can be avoided. Once the single planar fracture in the rock matrix is represented by a series of finite number of compartments having region wise constant parameter values in them, the medium is continuous in view of various processes associated with nuclide transport but discrete in medium space and such geologic system is assumed to have Markov property, since the Markov process requires that only the present value of the time dependent random variable be known to determine the future value of random variable, nuclide transport in the medium can then be modeled as a continuous time Markov process. Processes that are involved in nuclide transport are advective transport due to groundwater flow, diffusion into the rock matrix, adsorption onto the wall of the fracture and within the pores in the rock matrix, and radioactive decay chain. The transition probabilities for nuclide from the transition intensities between and out of the compartments are represented utilizing Chapman-Kolmogorov equation, through which the expectation and the variance of nuclide distribution for each compartment or the fractured rock medium can be obtained. Some comparisons between Markov process model developed in this work and available analytical solutions for one-dimensional layered porous medium, fractured medium with rock matrix diffusion, and porous medium considering three member nuclide decay chain without rock matrix diffusion have been made showing comparatively good agreement for all cases. To verify the model developed in this work another comparative study was also made by fitting the experimental data obtained with NaLS and uranine running in the artificial fractured
Stochastic space-time and quantum theory
International Nuclear Information System (INIS)
Frederick, C.
1976-01-01
Much of quantum mechanics may be derived if one adopts a very strong form of Mach's principle such that in the absence of mass, space-time becomes not flat, but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic-metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can obtain an explanation of conjugate variables and also a derivation of the uncertainty principle. Finally the superposition of stochastic metrics and the identification of root -g in the four-dimensional invariant volume element root -g dV as the indicator of relative probability yields the phenomenon of interference as will be described for the two-slit experiment
A Stochastic Model for Malaria Transmission Dynamics
Directory of Open Access Journals (Sweden)
Rachel Waema Mbogo
2018-01-01
Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.
Identifcation of a Linear COntinuous Time Stochastic Model of the Heat Dynamics of a Greenhouse
DEFF Research Database (Denmark)
Nielsen, Bjarne; Madsen, Henrik
1998-01-01
The purpose of this paper is to describe the basis for improving the control of air temperature and heat supply in greenhouses using a method which controls the energy supply by a model-based prediction of the air temperature in the greenhouse. Controllers of this type are the minimum variance co...... controller, the generalized predictive controller and the proportional-integral-plus(PIP) controller. Prediction-based controllers have proved to be powerful in controlling the supply temperature in a distinct heating system....
Manzione, Rodrigo L.; Wendland, Edson; Tanikawa, Diego H.
2012-11-01
Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.
Characterizing economic trends by Bayesian stochastic model specifi cation search
Grassi, Stefano; Proietti, Tommaso
2010-01-01
We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and deterministic trends. In particular, we formulate autoregressive models with stochastic trends components and decide on whether a specific feature of the series, i.e. the underlying level and/or the rate...
Stochastic diffusion models for substitutable technological innovations
Wang, L.; Hu, B.; Yu, X.
2004-01-01
Based on the analysis of firms' stochastic adoption behaviour, this paper first points out the necessity to build more practical stochastic models. And then, stochastic evolutionary models are built for substitutable innovation diffusion system. Finally, through the computer simulation of the
Research on nonlinear stochastic dynamical price model
International Nuclear Information System (INIS)
Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng
2008-01-01
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies
Multimodal Network Equilibrium with Stochastic Travel Times
Directory of Open Access Journals (Sweden)
M. Meng
2014-01-01
Full Text Available The private car, unlike public traffic modes (e.g., subway, trolley running along dedicated track-ways, is invariably subject to various uncertainties resulting in travel time variation. A multimodal network equilibrium model is formulated that explicitly considers stochastic link capacity variability in the road network. The travel time of combined-mode trips is accumulated based on the concept of the mean excess travel time (METT which is a summation of estimated buffer time and tardy time. The problem is characterized by an equivalent VI (variational inequality formulation where the mode choice is expressed in a hierarchical logit structure. Specifically, the supernetwork theory and expansion technique are used herein to represent the multimodal transportation network, which completely represents the combined-mode trips as constituting multiple modes within a trip. The method of successive weighted average is adopted for problem solutions. The model and solution method are further applied to study the trip distribution and METT variations caused by the different levels of the road conditions. Results of numerical examples show that travelers prefer to choose the combined travel mode as road capacity decreases. Travelers with different attitudes towards risk are shown to exhibit significant differences when making travel choice decisions.
Importance Sampling for Stochastic Timed Automata
DEFF Research Database (Denmark)
Jegourel, Cyrille; Larsen, Kim Guldstrand; Legay, Axel
2016-01-01
We present an importance sampling framework that combines symbolic analysis and simulation to estimate the probability of rare reachability properties in stochastic timed automata. By means of symbolic exploration, our framework first identifies states that cannot reach the goal. A state-wise cha......We present an importance sampling framework that combines symbolic analysis and simulation to estimate the probability of rare reachability properties in stochastic timed automata. By means of symbolic exploration, our framework first identifies states that cannot reach the goal. A state...
Stochastic models for atmospheric dispersion
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2003-01-01
Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... positions close to the boundaries. Different rules have been suggested in the literature with justifications based on simulation studies. Herein the relevant stochastic differential equation model is formulated in a particular way. The formulation is based on the marginal transformation of the position...... velocity distributions that depend on height above the ground both with respect to standard deviation and skewness are substituted into the stationary Fokker/Planck equation. The particle position distribution is taken to be uniform *the well/mixed condition( and also a given dispersion coefficient...
Stochastic resonance in models of neuronal ensembles
International Nuclear Information System (INIS)
Chialvo, D.R.; Longtin, A.; Mueller-Gerkin, J.
1997-01-01
Two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time-varying inputs are considered. It is shown, using theoretical arguments and numerical simulations, that the nonmonotonic behavior with increasing noise of the correlation measures used for the so-called aperiodic stochastic resonance (ASR) scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems. Rather, ASR with slowly varying signals is more properly interpreted as linearization by noise. Consequently, the broadening of the open-quotes resonance curveclose quotes in the multineuron stochastic resonance without tuning scenario can also be explained by this linearization. Computation of the input-output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise-induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise. Thus, our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals. It also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime. Finally, we show that the inclusion of a refractory period in the spike-detection scheme produces a better correlation between instantaneous firing rate and input signal. copyright 1997 The American Physical Society
Dynamic optimization deterministic and stochastic models
Hinderer, Karl; Stieglitz, Michael
2016-01-01
This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.
Directory of Open Access Journals (Sweden)
YouHua Chen
2014-06-01
Full Text Available In the present report, the coexistence of Prisoners' Dilemma game players (cooperators and defectors were explored in an individual-based framework with the consideration of the impacts of deterministic and stochastic waiting time (WT for triggering mortality and/or colonization events. For the type of deterministic waiting time, the time step for triggering a mortality and/or colonization event is fixed. For the type of stochastic waiting time, whether a mortality and/or colonization event should be triggered for each time step of a simulation is randomly determined by a given acceptance probability (the event takes place when a variate drawn from a uniform distribution [0,1] is smaller than the acceptance probability. The two strategies of modeling waiting time are considered simultaneously and applied to both quantities (mortality: WTm, colonization: WTc. As such, when WT (WTm and/or WTc is an integral >=1, it indicated a deterministically triggering strategy. In contrast, when 1>WT>0, it indicated a stochastically triggering strategy and the WT value itself is used as the acceptance probability. The parameter space between the waiting time for mortality (WTm-[0.1,40] and colonization (WTc-[0.1,40] was traversed to explore the coexistence and non-coexistence regions. The role of defense award was evaluated. My results showed that, one non-coexistence region is identified consistently, located at the area where 1>=WTm>=0.3 and 40>=WTc>=0.1. As a consequence, it was found that the coexistence of cooperators and defectors in the community is largely dependent on the waiting time of mortality events, regardless of the defense or cooperation rewards. When the mortality events happen in terms of stochastic waiting time (1>=WTm>=0.3, extinction of either cooperators or defectors or both could be very likely, leading to the emergence of non-coexistence scenarios. However, when the mortality events occur in forms of relatively long deterministic
Probability and stochastic modeling
Rotar, Vladimir I
2012-01-01
Basic NotionsSample Space and EventsProbabilitiesCounting TechniquesIndependence and Conditional ProbabilityIndependenceConditioningThe Borel-Cantelli TheoremDiscrete Random VariablesRandom Variables and VectorsExpected ValueVariance and Other Moments. Inequalities for DeviationsSome Basic DistributionsConvergence of Random Variables. The Law of Large NumbersConditional ExpectationGenerating Functions. Branching Processes. Random Walk RevisitedBranching Processes Generating Functions Branching Processes Revisited More on Random WalkMarkov ChainsDefinitions and Examples. Probability Distributions of Markov ChainsThe First Step Analysis. Passage TimesVariables Defined on a Markov ChainErgodicity and Stationary DistributionsA Classification of States and ErgodicityContinuous Random VariablesContinuous DistributionsSome Basic Distributions Continuous Multivariate Distributions Sums of Independent Random Variables Conditional Distributions and ExpectationsDistributions in the General Case. SimulationDistribution F...
Stochastic models in reliability and maintenance
2002-01-01
Our daily lives can be maintained by the high-technology systems. Computer systems are typical examples of such systems. We can enjoy our modern lives by using many computer systems. Much more importantly, we have to maintain such systems without failure, but cannot predict when such systems will fail and how to fix such systems without delay. A stochastic process is a set of outcomes of a random experiment indexed by time, and is one of the key tools needed to analyze the future behavior quantitatively. Reliability and maintainability technologies are of great interest and importance to the maintenance of such systems. Many mathematical models have been and will be proposed to describe reliability and maintainability systems by using the stochastic processes. The theme of this book is "Stochastic Models in Reliability and Main tainability. " This book consists of 12 chapters on the theme above from the different viewpoints of stochastic modeling. Chapter 1 is devoted to "Renewal Processes," under which cla...
Model predictive control classical, robust and stochastic
Kouvaritakis, Basil
2016-01-01
For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplic...
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Sequential neural models with stochastic layers
DEFF Research Database (Denmark)
Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich
2016-01-01
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...
A stochastic model of hormesis
International Nuclear Information System (INIS)
Yakovlev, A.Yu.; Tsodikov, A.D.; Bass, L.
1993-01-01
In order to describe the life-prolonging effect of some agents that are harmful at higher doses, ionizing radiations in particular, a stochastic model is developed in terms of accumulation and progression of intracellular lesions caused by the environment and by the agent itself. The processes of lesion repair, operating at the molecular and cellular level, are assumed to be responsible for this hormesis effect within the framework of the proposed model. Properties of lifetime distributions, derived for analysis of animal experiments with prolonged and acute irradiation, are given special attention. The model provides efficient means of interpreting experimental findings, as evidenced by its application to analysis of some published data on the hormetic effects of prolonged irradiation and of procaine on animal longevity. 51 refs., 2 figs., 1 tabs
Stochastic models for tumoral growth
Escudero, Carlos
2006-02-01
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border and the surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are reported in this paper in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantage of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. An analysis of these models allows us to quantitatively estimate the response of the tumor to an unfavorable perturbation during growth.
Discrete stochastic analogs of Erlang epidemic models.
Getz, Wayne M; Dougherty, Eric R
2018-12-01
Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.
CAM Stochastic Volatility Model for Option Pricing
Directory of Open Access Journals (Sweden)
Wanwan Huang
2016-01-01
Full Text Available The coupled additive and multiplicative (CAM noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks of the model. We also derive an approximation for the characteristic function of the model.
Gompertzian stochastic model with delay effect to cervical cancer growth
International Nuclear Information System (INIS)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-01-01
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits
Gompertzian stochastic model with delay effect to cervical cancer growth
Energy Technology Data Exchange (ETDEWEB)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor and UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-02-03
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Lu, M.; Lall, U.
2013-12-01
In order to mitigate the impacts of climate change, proactive management strategies to operate reservoirs and dams are needed. A multi-time scale climate informed stochastic model is developed to optimize the operations for a multi-purpose single reservoir by simulating decadal, interannual, seasonal and sub-seasonal variability. We apply the model to a setting motivated by the largest multi-purpose dam in N. India, the Bhakhra reservoir on the Sutlej River, a tributary of the Indus. This leads to a focus on timing and amplitude of the flows for the monsoon and snowmelt periods. The flow simulations are constrained by multiple sources of historical data and GCM future projections, that are being developed through a NSF funded project titled 'Decadal Prediction and Stochastic Simulation of Hydroclimate Over Monsoon Asia'. The model presented is a multilevel, nonlinear programming model that aims to optimize the reservoir operating policy on a decadal horizon and the operation strategy on an updated annual basis. The model is hierarchical, in terms of having a structure that two optimization models designated for different time scales are nested as a matryoshka doll. The two optimization models have similar mathematical formulations with some modifications to meet the constraints within that time frame. The first level of the model is designated to provide optimization solution for policy makers to determine contracted annual releases to different uses with a prescribed reliability; the second level is a within-the-period (e.g., year) operation optimization scheme that allocates the contracted annual releases on a subperiod (e.g. monthly) basis, with additional benefit for extra release and penalty for failure. The model maximizes the net benefit of irrigation, hydropower generation and flood control in each of the periods. The model design thus facilitates the consistent application of weather and climate forecasts to improve operations of reservoir systems. The
12th Workshop on Stochastic Models, Statistics and Their Applications
Rafajłowicz, Ewaryst; Szajowski, Krzysztof
2015-01-01
This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.
Directory of Open Access Journals (Sweden)
Bo Sun
2018-03-01
Full Text Available In the degradation process, the randomness and multiplicity of variables are difficult to describe by mathematical models. However, they are common in engineering and cannot be neglected, so it is necessary to study this issue in depth. In this paper, the copper bending pipe in seawater piping systems is taken as the analysis object, and the time-variant reliability is calculated by solving the interference of limit strength and maximum stress. We did degradation experiments and tensile experiments on copper material, and obtained the limit strength at each time. In addition, degradation experiments on copper bending pipe were done and the thickness at each time has been obtained, then the response of maximum stress was calculated by simulation. Further, with the help of one kind of Monte Carlo method we propose, the time-variant reliability of copper bending pipe was calculated based on the stochastic degradation process and interference theory. Compared with traditional methods and verified by maintenance records, the results show that the time-variant reliability model based on the stochastic degradation process proposed in this paper has better applicability in the reliability analysis, and it can be more convenient and accurate to predict the replacement cycle of copper bending pipe under seawater-active corrosion.
A stochastic model for quantum measurement
International Nuclear Information System (INIS)
Budiyono, Agung
2013-01-01
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system. (paper)
Consistent Stochastic Modelling of Meteocean Design Parameters
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Sterndorff, M. J.
2000-01-01
Consistent stochastic models of metocean design parameters and their directional dependencies are essential for reliability assessment of offshore structures. In this paper a stochastic model for the annual maximum values of the significant wave height, and the associated wind velocity, current...
Stochastic modeling of soil salinity
Suweis, S.; Porporato, A. M.; Daly, E.; van der Zee, S.; Maritan, A.; Rinaldo, A.
2010-12-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The equations for the probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equations to a single stochastic differential equation (generalized Langevin equation) driven by multiplicative Poisson noise. Generalized Langevin equations with multiplicative white Poisson noise pose the usual Ito (I) or Stratonovich (S) prescription dilemma. Different interpretations lead to different results and then choosing between the I and S prescriptions is crucial to describe correctly the dynamics of the model systems. We show how this choice can be determined by physical information about the timescales involved in the process. We also show that when the multiplicative noise is at most linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We then apply these results to the generalized Langevin equation that drives the salt mass dynamics. The stationary analytical solutions for the probability density functions of salt mass and concentration provide insight on the interplay of the main soil, plant and climate parameters responsible for long term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in longterm soil salinization trends, with significant consequences, e.g. for climate change impacts on rain fed agriculture.
Stochastic models for predicting pitting corrosion damage of HLRW containers
International Nuclear Information System (INIS)
Henshall, G.A.
1991-10-01
Stochastic models for predicting aqueous pitting corrosion damage of high-level radioactive-waste containers are described. These models could be used to predict the time required for the first pit to penetrate a container and the increase in the number of breaches at later times, both of which would be useful in the repository system performance analysis. Monte Carlo implementations of the stochastic models are described, and predictions of induction time, survival probability and pit depth distributions are presented. These results suggest that the pit nucleation probability decreases with exposure time and that pit growth may be a stochastic process. The advantages and disadvantages of the stochastic approach, methods for modeling the effects of environment, and plans for future work are discussed
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...
Jumps and stochastic volatility in oil prices: Time series evidence
International Nuclear Information System (INIS)
Larsson, Karl; Nossman, Marcus
2011-01-01
In this paper we examine the empirical performance of affine jump diffusion models with stochastic volatility in a time series study of crude oil prices. We compare four different models and estimate them using the Markov Chain Monte Carlo method. The support for a stochastic volatility model including jumps in both prices and volatility is strong and the model clearly outperforms the others in terms of a superior fit to data. Our estimation method allows us to obtain a detailed study of oil prices during two periods of extreme market stress included in our sample; the Gulf war and the recent financial crisis. We also address the economic significance of model choice in two option pricing applications. The implied volatilities generated by the different estimated models are compared and we price a real option to develop an oil field. Our findings indicate that model choice can have a material effect on the option values.
Stochastic model of energetic nuclear reactor
International Nuclear Information System (INIS)
Bojko, R.V.; Ryazanov, V.V.
2002-01-01
Behaviour of nuclear reactor was treated using the theory of branching processes. As mathematical model descriptive the neutron number in time the Markov occasional process is proposed. Application of branching occasional processes with variable regime to the description of neutron behaviour in the reactor makes possible conducting strong description of critical operation regime and demonstrates the severity of the process. Three regimes of the critical behaviour depending on the sign of manipulated variables and feedbacks were discovered. Probability regularities peculiar to the behaviour of the reactor are embodied to the suggested stochastic model [ru
Investment timing under hybrid stochastic and local volatility
International Nuclear Information System (INIS)
Kim, Jeong-Hoon; Lee, Min-Ku; Sohn, So Young
2014-01-01
Highlights: • The effects of hybrid stochastic volatility on real option prices are studied. • The stochastic volatility consists of a fast mean-reverting component and a CEV type one. • A fast mean-reverting factor lowers real option prices and investment thresholds. • The increase of elasticity raises real option prices and investment thresholds. • The effects of the addition of a slowly varying factor depend upon the project value. - Abstract: We consider an investment timing problem under a real option model where the instantaneous volatility of the project value is given by a combination of a hidden stochastic process and the project value itself. The stochastic volatility part is given by a function of a fast mean-reverting process as well as a slowly varying process and the local volatility part is a power (the elasticity parameter) of the project value itself. The elasticity parameter controls directly the correlation between the project value and the volatility. Knowing that the project value represents the market price of a real asset in many applications and the value of the elasticity parameter depends on the asset, the elasticity parameter should be treated with caution for investment decision problems. Based on the hybrid structure of volatility, we investigate the simultaneous impact of the elasticity and the stochastic volatility on the real option value as well as the investment threshold
Evoking prescribed spike times in stochastic neurons
Doose, Jens; Lindner, Benjamin
2017-09-01
Single cell stimulation in vivo is a powerful tool to investigate the properties of single neurons and their functionality in neural networks. We present a method to determine a cell-specific stimulus that reliably evokes a prescribed spike train with high temporal precision of action potentials. We test the performance of this stimulus in simulations for two different stochastic neuron models. For a broad range of parameters and a neuron firing with intermediate firing rates (20-40 Hz) the reliability in evoking the prescribed spike train is close to its theoretical maximum that is mainly determined by the level of intrinsic noise.
Quantum mechanics, stochasticity and space-time
International Nuclear Information System (INIS)
Ramanathan, R.
1986-04-01
An extended and more rigorous version of a recent proposal for an objective stochastic formulation of quantum mechanics along with its extension to the relativistic case without spin is presented. The relativistic Klein-Gordon equation is shown to be a particular form of the relativistic Kolmogorov-Fokker-Planck equation which is derived from a covariant formulation of the Chapman-Kolmogorov condition. Complexification of probability amplitudes is again achieved only through a conformal rotation of Minkowski space-time M 4 . (author)
Fitting PAC spectra with stochastic models: PolyPacFit
Energy Technology Data Exchange (ETDEWEB)
Zacate, M. O., E-mail: zacatem1@nku.edu [Northern Kentucky University, Department of Physics and Geology (United States); Evenson, W. E. [Utah Valley University, College of Science and Health (United States); Newhouse, R.; Collins, G. S. [Washington State University, Department of Physics and Astronomy (United States)
2010-04-15
PolyPacFit is an advanced fitting program for time-differential perturbed angular correlation (PAC) spectroscopy. It incorporates stochastic models and provides robust options for customization of fits. Notable features of the program include platform independence and support for (1) fits to stochastic models of hyperfine interactions, (2) user-defined constraints among model parameters, (3) fits to multiple spectra simultaneously, and (4) any spin nuclear probe.
Stochastic quantization for the axial model
International Nuclear Information System (INIS)
Farina, C.; Montani, H.; Albuquerque, L.C.
1991-01-01
We use bosonization ideas to solve the axial model in the stochastic quantization framework. We obtain the fermion propagator of the theory decoupling directly the Langevin equation, instead of the Fokker-Planck equation. In the Appendix we calculate explicitly the anomalous divergence of the axial-vector current by using a regularization that does not break the Markovian character of the stochastic process
A compositional Translation of Stochastic Automata into Timed Automata
d' Argenio, P.R.
We present a translation from stochastic automata [17, 16] into timed automata with deadlines [37, 13]. The translation preserves traces when the stochastic characteristics, namely the probability measures, are abstracted from the original stochastic automaton. Moreover, we show that the translation
Stochastic models of intracellular transport
Bressloff, Paul C.
2013-01-09
The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of adenosine triphosphate hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review a wide range of analytical methods and models of intracellular transport is presented. In the case of diffusive transport, narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion are considered. In the case of active transport, Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean-field approximations are considered. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures. © 2013 American Physical Society.
STOCHASTIC CHARACTERISTICS AND MODELING OF RELATIVE ...
African Journals Online (AJOL)
Test
Results are highly accurate and promising for all models based on Lewis' criteria. ... hydrological cycle. Future increases in ... STOCHASTIC CHARACTERISTICS AND MODELING OF RELATIVE HUMIDITY OF OGUN BASIN, NIGERIA. 71 ...
Towards Model Checking Stochastic Process Algebra
Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.
2000-01-01
Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of
Stochastic ℋ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.
Stochastic biomathematical models with applications to neuronal modeling
Batzel, Jerry; Ditlevsen, Susanne
2013-01-01
Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.
Time-adaptive and history-adaptive multicriterion routing in stochastic, time-dependent networks
DEFF Research Database (Denmark)
Pretolani, Daniele; Nielsen, Lars Relund; Andersen, Kim Allan
2009-01-01
We compare two different models for multicriterion routing in stochastic time-dependent networks: the classic "time-adaptive'' model and the more flexible "history-adaptive'' one. We point out several properties of the sets of efficient solutions found under the two models. We also devise a method...
Stochasticity and determinism in models of hematopoiesis.
Kimmel, Marek
2014-01-01
This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.
Stochastic calculus for uncoupled continuous-time random walks.
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L
2009-06-01
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy alpha -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.
Vehicle routing with stochastic time-dependent travel times
Lecluyse, C.; Woensel, van T.; Peremans, H.
2009-01-01
Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the
Vehicle routing with stochastic time-dependent travel times
Lecluyse, C.; Woensel, van T.; Peremans, H.
2007-01-01
Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the
Stochastic Modelling of Shiroro River Stream flow Process
Musa, J. J
2013-01-01
Economists, social scientists and engineers provide insights into the drivers of anthropogenic climate change and the options for adaptation and mitigation, and yet other scientists, including geographers and biologists, study the impacts of climate change. This project concentrates mainly on the discharge from the Shiroro River. A stochastic approach is presented for modeling a time series by an Autoregressive Moving Average model (ARMA). The development and use of a stochastic stream flow m...
Numerical Simulation of the Heston Model under Stochastic Correlation
Directory of Open Access Journals (Sweden)
Long Teng
2017-12-01
Full Text Available Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.
Scalable inference for stochastic block models
Peng, Chengbin
2017-12-08
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference algorithms for such a model are increasingly limited due to their high time complexity and poor scalability. In this paper, we propose a multi-stage maximum likelihood approach to recover the latent parameters of the stochastic block model, in time linear with respect to the number of edges. We also propose a parallel algorithm based on message passing. Our algorithm can overlap communication and computation, providing speedup without compromising accuracy as the number of processors grows. For example, to process a real-world graph with about 1.3 million nodes and 10 million edges, our algorithm requires about 6 seconds on 64 cores of a contemporary commodity Linux cluster. Experiments demonstrate that the algorithm can produce high quality results on both benchmark and real-world graphs. An example of finding more meaningful communities is illustrated consequently in comparison with a popular modularity maximization algorithm.
Stochastic Model Checking of the Stochastic Quality Calculus
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin
2015-01-01
The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input....... This gives rise to Generalised Semi-Markov Decision Processes for which few analytical techniques are available. We restrict delays on output actions to be exponentially distributed while still admitting real-time constraints on the quality binders. This facilitates developing analytical techniques based...
Scalable inference for stochastic block models
Peng, Chengbin; Zhang, Zhihua; Wong, Ka-Chun; Zhang, Xiangliang; Keyes, David E.
2017-01-01
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference
Stochastic interest rates model in compounding | Galadima ...
African Journals Online (AJOL)
Stochastic interest rates model in compounding. ... in finance, real estate, insurance, accounting and other areas of business administration. The assumption that future rates are fixed and known with certainty at the beginning of an investment, ...
Moment Closure for the Stochastic Logistic Model
National Research Council Canada - National Science Library
Singh, Abhyudai; Hespanha, Joao P
2006-01-01
..., which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model...
Modelling the stochastic behaviour of primary nucleation.
Maggioni, Giovanni Maria; Mazzotti, Marco
2015-01-01
We study the stochastic nature of primary nucleation and how it manifests itself in a crystallisation process at different scales and under different operating conditions. Such characteristics of nucleation are evident in many experiments where detection times of crystals are not identical, despite identical experimental conditions, but instead are distributed around an average value. While abundant experimental evidence has been reported in the literature, a clear theoretical understanding and an appropriate modelling of this feature is still missing. In this contribution, we present two models describing a batch cooling crystallisation, where the interplay between stochastic nucleation and deterministic crystal growth is described differently in each. The nucleation and growth rates of the two models are estimated by a comprehensive set of measurements of paracetamol crystallisation from aqueous solution in a 1 mL vessel [Kadam et al., Chemical Engineering Science, 2012, 72, 10-19]. Both models are applied to the cooling crystallisation process above under different operating conditions, i.e. different volumes, initial concentrations, cooling rates. The advantages and disadvantages of the two approaches are illustrated and discussed, with particular reference to their use across scales of nucleation rate measured in very small crystallisers.
A stochastic model of enzyme kinetics
Stefanini, Marianne; Newman, Timothy; McKane, Alan
2003-10-01
Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.
Stochastic Model of TCP SYN Attacks
Directory of Open Access Journals (Sweden)
Simona Ramanauskaitė
2011-08-01
Full Text Available A great proportion of essential services are moving into internet space making the threat of DoS attacks even more actual. To estimate the real risk of some kind of denial of service (DoS attack in real world is difficult, but mathematical and software models make this task easier. In this paper we overview the ways of implementing DoS attack models and offer a stochastic model of SYN flooding attack. It allows evaluating the potential threat of SYN flooding attacks, taking into account both the legitimate system flow as well as the possible attack power. At the same time we can assess the effect of such parameters as buffer capacity, open connection storage in the buffer or filtering efficiency on the success of different SYN flooding attacks. This model can be used for other type of memory depletion denial of service attacks.Article in Lithuanian
Stochastic first passage time accelerated with CUDA
Pierro, Vincenzo; Troiano, Luigi; Mejuto, Elena; Filatrella, Giovanni
2018-05-01
The numerical integration of stochastic trajectories to estimate the time to pass a threshold is an interesting physical quantity, for instance in Josephson junctions and atomic force microscopy, where the full trajectory is not accessible. We propose an algorithm suitable for efficient implementation on graphical processing unit in CUDA environment. The proposed approach for well balanced loads achieves almost perfect scaling with the number of available threads and processors, and allows an acceleration of about 400× with a GPU GTX980 respect to standard multicore CPU. This method allows with off the shell GPU to challenge problems that are otherwise prohibitive, as thermal activation in slowly tilted potentials. In particular, we demonstrate that it is possible to simulate the switching currents distributions of Josephson junctions in the timescale of actual experiments.
Characterizing economic trends by Bayesian stochastic model specification search
DEFF Research Database (Denmark)
Grassi, Stefano; Proietti, Tommaso
We extend a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. In particular, we focus on autoregressive models with possibly time-varying intercept and slope and decide on ...
Modelling Cow Behaviour Using Stochastic Automata
DEFF Research Database (Denmark)
Jónsson, Ragnar Ingi
This report covers an initial study on the modelling of cow behaviour using stochastic automata with the aim of detecting lameness. Lameness in cows is a serious problem that needs to be dealt with because it results in less profitable production units and in reduced quality of life...... for the affected livestock. By featuring training data consisting of measurements of cow activity, three different models are obtained, namely an autonomous stochastic automaton, a stochastic automaton with coinciding state and output and an autonomous stochastic automaton with coinciding state and output, all...... of which describe the cows' activity in the two regarded behavioural scenarios, non-lame and lame. Using the experimental measurement data the different behavioural relations for the two regarded behavioural scenarios are assessed. The three models comprise activity within last hour, activity within last...
A stochastic SIS epidemic model with vaccination
Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming
2017-11-01
In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.
Intimate Partner Violence: A Stochastic Model.
Guidi, Elisa; Meringolo, Patrizia; Guazzini, Andrea; Bagnoli, Franco
2017-01-01
Intimate partner violence (IPV) has been a well-studied problem in the past psychological literature, especially through its classical methodology such as qualitative, quantitative and mixed methods. This article introduces two basic stochastic models as an alternative approach to simulate the short and long-term dynamics of a couple at risk of IPV. In both models, the members of the couple may assume a finite number of states, updating them in a probabilistic way at discrete time steps. After defining the transition probabilities, we first analyze the evolution of the couple in isolation and then we consider the case in which the individuals modify their behavior depending on the perceived violence from other couples in their environment or based on the perceived informal social support. While high perceived violence in other couples may converge toward the own presence of IPV by means a gender-specific transmission, the gender differences fade-out in the case of received informal social support. Despite the simplicity of the two stochastic models, they generate results which compare well with past experimental studies about IPV and they give important practical implications for prevention intervention in this field. Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.
Stochastic inflation as a time-dependent random walk
International Nuclear Information System (INIS)
Kandrup, H.E.
1989-01-01
This paper exploits the ''stochastic inflation'' paradigm introduced by Starobinskii to study the evolution of long-wavelength modes for a free scalar field Phi in an inflationary Universe. By relaxing the assumption of a ''slow roll,'' it becomes obvious that the well-known late-time infrared divergence of the vacuum for a massless field in de Sitter space may be viewed as a consequence of the fluctuation-dissipation theorem. This stochastic model is also extended to allow for nonvacuum states and power-law inflation, situations where the fluctuation-dissipation theorem no longer holds. One recovers the correct late-time form for the expectation value 2 > in these cases as well, corroborating thereby the intuitive picture that, quite generally, the long-wavelength modes of the field evolve in a thermal ''bath'' provided by the shorter-wavelength modes
Stochastic Wake Modelling Based on POD Analysis
Directory of Open Access Journals (Sweden)
David Bastine
2018-03-01
Full Text Available In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD, three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained.
Stochastic modeling of thermal fatigue crack growth
Radu, Vasile
2015-01-01
The book describes a systematic stochastic modeling approach for assessing thermal-fatigue crack-growth in mixing tees, based on the power spectral density of temperature fluctuation at the inner pipe surface. It shows the development of a frequency-temperature response function in the framework of single-input, single-output (SISO) methodology from random noise/signal theory under sinusoidal input. The frequency response of stress intensity factor (SIF) is obtained by a polynomial fitting procedure of thermal stress profiles at various instants of time. The method, which takes into account the variability of material properties, and has been implemented in a real-world application, estimates the probabilities of failure by considering a limit state function and Monte Carlo analysis, which are based on the proposed stochastic model. Written in a comprehensive and accessible style, this book presents a new and effective method for assessing thermal fatigue crack, and it is intended as a concise and practice-or...
Stochastic modeling of financial electricity contracts
International Nuclear Information System (INIS)
Benth, Fred Espen; Koekebakker, Steen
2008-01-01
We discuss the modeling of electricity contracts traded in many deregulated power markets. These forward/futures type contracts deliver (either physically or financially) electricity over a specified time period, and is frequently referred to as swaps since they in effect represent an exchange of fixed for floating electricity price. We propose to use the Heath-Jarrow-Morton approach to model swap prices since the notion of a spot price is not easily defined in these markets. For general stochastic dynamical models, we connect the spot price, the instantaneous-delivery forward price and the swap price, and analyze two different ways to apply the Heath-Jarrow-Morton approach to swap pricing: Either one specifies a dynamics for the non-existing instantaneous-delivery forwards and derives the implied swap dynamics, or one models directly on the swaps. The former is shown to lead to quite complicated stochastic models for the swap price, even when the forward dynamics is simple. The latter has some theoretical problems due to a no-arbitrage condition that has to be satisfied for swaps with overlapping delivery periods. To overcome this problem, a practical modeling approach is analyzed. The market is supposed only to consist of non-overlapping swaps, and these are modelled directly. A thorough empirical study is performed using data collected from Nord Pool. Our investigations demonstrate that it is possible to state reasonable models for the swap price dynamics which is analytically tractable for risk management and option pricing purposes, however, this is an area of further research. (author)
Directory of Open Access Journals (Sweden)
Yanhui Li
2014-01-01
Full Text Available This paper investigates the Hankel norm filter design problem for stochastic time-delay systems, which are represented by Takagi-Sugeno (T-S fuzzy model. Motivated by the parallel distributed compensation (PDC technique, a novel filtering error system is established. The objective is to design a suitable filter that guarantees the corresponding filtering error system to be mean-square asymptotically stable and to have a specified Hankel norm performance level γ. Based on the Lyapunov stability theory and the Itô differential rule, the Hankel norm criterion is first established by adopting the integral inequality method, which can make some useful efforts in reducing conservativeness. The Hankel norm filtering problem is casted into a convex optimization problem with a convex linearization approach, which expresses all the conditions for the existence of admissible Hankel norm filter as standard linear matrix inequalities (LMIs. The effectiveness of the proposed method is demonstrated via a numerical example.
Double diffusivity model under stochastic forcing
Chattopadhyay, Amit K.; Aifantis, Elias C.
2017-05-01
The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...
Stochastic Modeling of Traffic Air Pollution
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
2014-01-01
In this paper, modeling of traffic air pollution is discussed with special reference to infrastructures. A number of subjects related to health effects of air pollution and the different types of pollutants are briefly presented. A simple model for estimating the social cost of traffic related air...... and using simple Monte Carlo techniques to obtain a stochastic estimate of the costs of traffic air pollution for infrastructures....... pollution is derived. Several authors have published papers on this very complicated subject, but no stochastic modelling procedure have obtained general acceptance. The subject is discussed basis of a deterministic model. However, it is straightforward to modify this model to include uncertain parameters...
Stochastic bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
Directory of Open Access Journals (Sweden)
Huynh Trung Luong
2016-11-01
Full Text Available In a continuous manufacturing environment where production and consumption occur simultaneously, one of the biggest challenges is the efficient management of production and inventory system. In order to manage the integrated production inventory system economically it is necessary to identify the optimal production time and the optimal production reorder point that either maximize the profit or minimize the cost. In addition, during production the process has to go through some natural phenomena like random breakdown of machine, deterioration of product over time, uncertainty in repair time that eventually create the possibility of shortage. In this situation, efficient management of inventory & production is crucial. This paper addresses the situation where a perishable (deteriorated product is manufactured and consumed simultaneously, the demand of this product is stable over the time, machine that produce the product also face random failure and the time to repair this machine is also uncertain. In order to describe this scenario more appropriately, the continuously reviewed Economic Production Quantity (EPQ model is considered in this research work. The main goal is to identify the optimal production uptime and the production reorder point that ultimately minimize the expected value of total cost consisting of machine setup, deterioration, inventory holding, shortage and corrective maintenance cost.
Stochastic fractional differential equations: Modeling, method and analysis
International Nuclear Information System (INIS)
Pedjeu, Jean-C.; Ladde, Gangaram S.
2012-01-01
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.
Time-variant reliability assessment through equivalent stochastic process transformation
International Nuclear Information System (INIS)
Wang, Zequn; Chen, Wei
2016-01-01
Time-variant reliability measures the probability that an engineering system successfully performs intended functions over a certain period of time under various sources of uncertainty. In practice, it is computationally prohibitive to propagate uncertainty in time-variant reliability assessment based on expensive or complex numerical models. This paper presents an equivalent stochastic process transformation approach for cost-effective prediction of reliability deterioration over the life cycle of an engineering system. To reduce the high dimensionality, a time-independent reliability model is developed by translating random processes and time parameters into random parameters in order to equivalently cover all potential failures that may occur during the time interval of interest. With the time-independent reliability model, an instantaneous failure surface is attained by using a Kriging-based surrogate model to identify all potential failure events. To enhance the efficacy of failure surface identification, a maximum confidence enhancement method is utilized to update the Kriging model sequentially. Then, the time-variant reliability is approximated using Monte Carlo simulations of the Kriging model where system failures over a time interval are predicted by the instantaneous failure surface. The results of two case studies demonstrate that the proposed approach is able to accurately predict the time evolution of system reliability while requiring much less computational efforts compared with the existing analytical approach. - Highlights: • Developed a new approach for time-variant reliability analysis. • Proposed a novel stochastic process transformation procedure to reduce the dimensionality. • Employed Kriging models with confidence-based adaptive sampling scheme to enhance computational efficiency. • The approach is effective for handling random process in time-variant reliability analysis. • Two case studies are used to demonstrate the efficacy
International Nuclear Information System (INIS)
Botterud, Audun; Korpaas, Magnus
2007-01-01
In this paper we formulate the power generation investment problem for a decentralised and profit-maximising investor operating in a restructured and competitive power system. In particular, we look at how uncertainty influences the optimal timing of investments in new power generation capacity. A real options approach is used to take long-term uncertainty in load growth, and its influence on future electricity prices, into account in the investment optimisation. In order to value the operational flexibility of a new power plant we use an electricity price model, where the spot price is a function of load level and installed generation capacity, in addition to short-term uncertainties and temporal fluctuations in the market. The investor's income from a capacity payment, which also can depend on the system's total capacity balance, can also be represented. Hence, with the optimisation model we can analyse power plant profitability and optimal timing of new investments under different market designs. In a case study from the Nordic electricity market we analyse the effect of uncertainty on optimal investment timing. We also examine how a fixed or variable capacity payment would influence the investment decision, and discuss the system consequences of the resulting investment strategies. (author)
Infinite-degree-corrected stochastic block model
DEFF Research Database (Denmark)
Herlau, Tue; Schmidt, Mikkel Nørgaard; Mørup, Morten
2014-01-01
In stochastic block models, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman [Karrer and Newman...... corrected stochastic block model as a nonparametric Bayesian model, incorporating a parameter to control the amount of degree correction that can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links...
CSL model checking of deterministic and stochastic Petri nets
Martinez Verdugo, J.M.; Haverkort, Boudewijn R.H.M.; German, R.; Heindl, A.
2006-01-01
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under
Directory of Open Access Journals (Sweden)
Guido Gigante
2015-11-01
Full Text Available Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them has been variously recognized in previous works as expression of the excitability of the cortical tissue and the associated nonlinear dynamics, a unified picture of the determinant factors (dynamical and architectural is desirable and not yet available. Progress has also been partially hindered by the use of a variety of statistical measures to define the network events of interest. We propose here a common probabilistic definition of network events that, applied to the firing activity of cultured neural networks, highlights the co-occurrence of network spikes, power-law distributed avalanches, and exponentially distributed 'quasi-orbits', which offer a third type of collective behavior. A rate model, including synaptic excitation and inhibition with no imposed topology, synaptic short-term depression, and finite-size noise, accounts for all these different, coexisting phenomena. We find that their emergence is largely regulated by the proximity to an oscillatory instability of the dynamics, where the non-linear excitable behavior leads to a self-amplification of activity fluctuations over a wide range of scales in space and time. In this sense, the cultured network dynamics is compatible with an excitation-inhibition balance corresponding to a slightly sub-critical regime. Finally, we propose and test a method to infer the characteristic time of the fatigue process, from the observed time course of the network's firing rate. Unlike the model, possessing a single fatigue mechanism, the cultured network appears to show multiple time scales, signalling the possible coexistence of different fatigue mechanisms.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Directory of Open Access Journals (Sweden)
A. Valor
2013-01-01
Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Valor, A.; Caleyo, F.; Alfonso, L.; Velázquez, J. C.; Hallen, J. M.
2013-01-01
The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure ...
Stochastic volatility models and Kelvin waves
Energy Technology Data Exchange (ETDEWEB)
Lipton, Alex [Merrill Lynch, Mlfc Main, 2 King Edward Street, London EC1A 1HQ (United Kingdom); Sepp, Artur [Merrill Lynch, 4 World Financial Center, New York, NY 10080 (United States)], E-mail: Alex_Lipton@ml.com, E-mail: Artur_Sepp@ml.com
2008-08-29
We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.
Stochastic volatility models and Kelvin waves
Lipton, Alex; Sepp, Artur
2008-08-01
We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.
Stochastic volatility models and Kelvin waves
International Nuclear Information System (INIS)
Lipton, Alex; Sepp, Artur
2008-01-01
We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics
Deterministic and stochastic CTMC models from Zika disease transmission
Zevika, Mona; Soewono, Edy
2018-03-01
Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.
Stochastic Modeling Of Wind Turbine Drivetrain Components
DEFF Research Database (Denmark)
Rafsanjani, Hesam Mirzaei; Sørensen, John Dalsgaard
2014-01-01
reliable components are needed for wind turbine. In this paper focus is on reliability of critical components in drivetrain such as bearings and shafts. High failure rates of these components imply a need for more reliable components. To estimate the reliability of these components, stochastic models...... are needed for initial defects and damage accumulation. In this paper, stochastic models are formulated considering some of the failure modes observed in these components. The models are based on theoretical considerations, manufacturing uncertainties, size effects of different scales. It is illustrated how...
INFERENCE AND SENSITIVITY IN STOCHASTIC WIND POWER FORECAST MODELS.
Elkantassi, Soumaya
2017-10-03
Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.
INFERENCE AND SENSITIVITY IN STOCHASTIC WIND POWER FORECAST MODELS.
Elkantassi, Soumaya; Kalligiannaki, Evangelia; Tempone, Raul
2017-01-01
Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.
Introduction to modeling and analysis of stochastic systems
Kulkarni, V G
2011-01-01
This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany...
Stochastic modeling of sunshine number data
Energy Technology Data Exchange (ETDEWEB)
Brabec, Marek, E-mail: mbrabec@cs.cas.cz [Department of Nonlinear Modeling, Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou vezi 2, 182 07 Prague 8 (Czech Republic); Paulescu, Marius [Physics Department, West University of Timisoara, V. Parvan 4, 300223 Timisoara (Romania); Badescu, Viorel [Candida Oancea Institute, Polytechnic University of Bucharest, Spl. Independentei 313, 060042 Bucharest (Romania)
2013-11-13
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Stochastic modeling of sunshine number data
Brabec, Marek; Paulescu, Marius; Badescu, Viorel
2013-11-01
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Stochastic modeling of sunshine number data
International Nuclear Information System (INIS)
Brabec, Marek; Paulescu, Marius; Badescu, Viorel
2013-01-01
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
An adaptive stochastic model for financial markets
International Nuclear Information System (INIS)
Hernández, Juan Antonio; Benito, Rosa Marı´a; Losada, Juan Carlos
2012-01-01
An adaptive stochastic model is introduced to simulate the behavior of real asset markets. The model adapts itself by changing its parameters automatically on the basis of the recent historical data. The basic idea underlying the model is that a random variable uniformly distributed within an interval with variable extremes can replicate the histograms of asset returns. These extremes are calculated according to the arrival of new market information. This adaptive model is applied to the daily returns of three well-known indices: Ibex35, Dow Jones and Nikkei, for three complete years. The model reproduces the histograms of the studied indices as well as their autocorrelation structures. It produces the same fat tails and the same power laws, with exactly the same exponents, as in the real indices. In addition, the model shows a great adaptation capability, anticipating the volatility evolution and showing the same volatility clusters observed in the assets. This approach provides a novel way to model asset markets with internal dynamics which changes quickly with time, making it impossible to define a fixed model to fit the empirical observations.
Interplanetary Alfvenic fluctuations: A stochastic model
International Nuclear Information System (INIS)
Barnes, A.
1981-01-01
The strong alignment of the average directions of minimum magnetic variance and mean magnetic field in interplanetary Alfvenic fluctuations is inconsistent with the usual wave-propagation models. We investigate the concept of minimum variance for nonplanar Alfvenic fluctuations in which the field direction varies stochastically. It is found that the tendency of the minimum variance and mean field directions to be aligned may be purely a consequence of the randomness of the field direction. In particular, a well-defined direction of minimum variance does not imply that the fluctuations are necessarily planar. The fluctuation power spectrum is a power law for frequencies much higher than the inverse of the correlation time. The probability distribution of directions a randomly fluctuating field of constant magnitude is calculated. A new approach for observational studies of interplanetary fluctuations is suggested
Compositional Modelling of Stochastic Hybrid Systems
Strubbe, S.N.
2005-01-01
In this thesis we present a modelling framework for compositional modelling of stochastic hybrid systems. Hybrid systems consist of a combination of continuous and discrete dynamics. The state space of a hybrid system is hybrid in the sense that it consists of a continuous component and a discrete
Some recent developments in stochastic volatility modelling
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Nicolato, Elisa; Shephard, N.
2002-01-01
This paper reviews and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power variation...
Stochastic models for turbulent reacting flows
Energy Technology Data Exchange (ETDEWEB)
Kerstein, A. [Sandia National Laboratories, Livermore, CA (United States)
1993-12-01
The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.
Predicting Footbridge Response using Stochastic Load Models
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2013-01-01
Walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. are basically stochastic, although it is quite common to adapt deterministic models for these parameters. The present paper considers a stochastic approach to modeling the action of pedestrians, but when doing so...... decisions need to be made in terms of statistical distributions of walking parameters and in terms of the parameters describing the statistical distributions. The paper explores how sensitive computations of bridge response are to some of the decisions to be made in this respect. This is useful...
Stochastic models for transport in a fluidized bed
Dehling, H.G; Hoffmann, A.C; Stuut, H.W.
1999-01-01
In this paper we study stochastic models for the transport of particles in a fluidized bed reactor and compute the associated residence time distribution (RTD). Our main model is basically a diffusion process in [0;A] with reflecting/absorbing boundary conditions, modified by allowing jumps to the
Ranking shortest paths in Stochastic time-denpendent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele
A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...
K shortest paths in stochastic time-dependent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Pretolani, Daniele; Andersen, Kim Allan
2004-01-01
A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...
Modeling stochasticity in biochemical reaction networks
International Nuclear Information System (INIS)
Constantino, P H; Vlysidis, M; Smadbeck, P; Kaznessis, Y N
2016-01-01
Small biomolecular systems are inherently stochastic. Indeed, fluctuations of molecular species are substantial in living organisms and may result in significant variation in cellular phenotypes. The chemical master equation (CME) is the most detailed mathematical model that can describe stochastic behaviors. However, because of its complexity the CME has been solved for only few, very small reaction networks. As a result, the contribution of CME-based approaches to biology has been very limited. In this review we discuss the approach of solving CME by a set of differential equations of probability moments, called moment equations. We present different approaches to produce and to solve these equations, emphasizing the use of factorial moments and the zero information entropy closure scheme. We also provide information on the stability analysis of stochastic systems. Finally, we speculate on the utility of CME-based modeling formalisms, especially in the context of synthetic biology efforts. (topical review)
Stochastic linear programming models, theory, and computation
Kall, Peter
2011-01-01
This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...
Stochastic models of the Social Security trust funds.
Burdick, Clark; Manchester, Joyce
Each year in March, the Board of Trustees of the Social Security trust funds reports on the current and projected financial condition of the Social Security programs. Those programs, which pay monthly benefits to retired workers and their families, to the survivors of deceased workers, and to disabled workers and their families, are financed through the Old-Age, Survivors, and Disability Insurance (OASDI) Trust Funds. In their 2003 report, the Trustees present, for the first time, results from a stochastic model of the combined OASDI trust funds. Stochastic modeling is an important new tool for Social Security policy analysis and offers the promise of valuable new insights into the financial status of the OASDI trust funds and the effects of policy changes. The results presented in this article demonstrate that several stochastic models deliver broadly consistent results even though they use very different approaches and assumptions. However, they also show that the variation in trust fund outcomes differs as the approach and assumptions are varied. Which approach and assumptions are best suited for Social Security policy analysis remains an open question. Further research is needed before the promise of stochastic modeling is fully realized. For example, neither parameter uncertainty nor variability in ultimate assumption values is recognized explicitly in the analyses. Despite this caveat, stochastic modeling results are already shedding new light on the range and distribution of trust fund outcomes that might occur in the future.
Stochastic dynamical models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik
the physical and biological knowledge of the system, and nonlinearities introduced here can generate regime shifts or enhance the probability of regime shifts in the case of stochastic models, typically characterized by a threshold value for the known driver. A simple model for light competition between...... definition and stability of regimes become less subtle. Ecological regime shifts and their modeling must be viewed in a probabilistic manner, particularly if such model results are to be used in ecosystem management....
Modeling animal movements using stochastic differential equations
Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie
2004-01-01
We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...
Stochastic Load Models and Footbridge Response
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2015-01-01
Pedestrians may cause vibrations in footbridges and these vibrations may potentially be annoying. This calls for predictions of footbridge vibration levels and the paper considers a stochastic approach to modeling the action of pedestrians assuming walking parameters such as step frequency, pedes...
Stochastic Growth Models with No Discounting
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2007-01-01
Roč. 15, č. 4 (2007), s. 88-98 ISSN 0572-3043 R&D Projects: GA ČR(CZ) GA402/06/0990; GA ČR GA402/05/0115 Institutional research plan: CEZ:AV0Z10750506 Keywords : economic dynamics * stochastic version of the Ramsey growth model * Markov decision processes Subject RIV: AH - Economics
Directory of Open Access Journals (Sweden)
Elisa Alòs
2008-01-01
Full Text Available We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.
Distributed parallel computing in stochastic modeling of groundwater systems.
Dong, Yanhui; Li, Guomin; Xu, Haizhen
2013-03-01
Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.
2011-05-12
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.; Heemink, A.W.; Verlaan, M.; Hoteit, Ibrahim
2011-01-01
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
Stochastic model of the spinning electron
International Nuclear Information System (INIS)
Simaciu, I.; Borsos, Z.
2002-01-01
In Stochastic Electrodynamics (SED) it is demonstrated that electrostatic interaction is the result of the scattering of the Classical Zero-Point Field (CZPF) background by the charged particles. In such models, the electron is modelled as a two-dimensional oscillator, which interacts with the electric component of the CZPF background. The electron with spin is not only an electric monopole but also a magnetic dipole. The interaction of the spin electron with the CZPF background is not only electric but also magnetic. We calculate the scattering cross-section of magnetic dipole in the situation when a magnetic field, variable in time B arrow = B 0 arrow sin ωt, acts over the rigid magnetic dipole given by the symmetry of the model. The cross-section of a magnetic dipole σ m must be equal to the cross-section of an electric monopole σ e . This equality between σ m and σ e cross-sections is motivated, too, by the fact that, in the model of the two-dimensional oscillator, the electric charge q e has the motion speed c. (authors)
Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models
International Nuclear Information System (INIS)
Eyink, Gregory L.
2009-01-01
We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.
Deterministic and stochastic models for middle east respiratory syndrome (MERS)
Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning
2018-03-01
World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.
News Impact Curve for Stochastic Volatility Models
Makoto Takahashi; Yasuhiro Omori; Toshiaki Watanabe
2012-01-01
This paper proposes a new method to compute the news impact curve for stochastic volatility (SV) models. The new method incorporates the joint movement of return and volatility, which has been ignored by the extant literature, by simply adding a couple of steps to the Bayesian MCMC estimation procedures for SV models. This simple procedure is versatile and applicable to various SV type models. Contrary to the monotonic news impact functions in the extant literature, the new method gives a U-s...
Reversibility in Quantum Models of Stochastic Processes
Gier, David; Crutchfield, James; Mahoney, John; James, Ryan
Natural phenomena such as time series of neural firing, orientation of layers in crystal stacking and successive measurements in spin-systems are inherently probabilistic. The provably minimal classical models of such stochastic processes are ɛ-machines, which consist of internal states, transition probabilities between states and output values. The topological properties of the ɛ-machine for a given process characterize the structure, memory and patterns of that process. However ɛ-machines are often not ideal because their statistical complexity (Cμ) is demonstrably greater than the excess entropy (E) of the processes they represent. Quantum models (q-machines) of the same processes can do better in that their statistical complexity (Cq) obeys the relation Cμ >= Cq >= E. q-machines can be constructed to consider longer lengths of strings, resulting in greater compression. With code-words of sufficiently long length, the statistical complexity becomes time-symmetric - a feature apparently novel to this quantum representation. This result has ramifications for compression of classical information in quantum computing and quantum communication technology.
A stochastic model for forecast consumption in master scheduling
Weeda, P.J.; Weeda, P.J.
1994-01-01
This paper describes a stochastic model for the reduction of the initial forecast in the Master Schedule (MS) of an MRP system during progress of time by the acceptance of customer orders. Results are given for the expectation and variance of the number of yet unknown deliveries as a function of
2014-01-01
M.Com. (Financial Economics) Recently, there has been a growth in the bond market. This growth has brought with it an ever-increasing volume and range of interest rate depended derivative products known as interest rate derivatives. Amongst the variables used in pricing these derivative products is the short-term interest rate. A numbers of short-term interest rate models that are used to fit the short-term interest rate exist. Therefore, understanding the features characterised by various...
A hierarchical stochastic model for bistable perception.
Directory of Open Access Journals (Sweden)
Stefan Albert
2017-11-01
Full Text Available Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM, which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group
A hierarchical stochastic model for bistable perception.
Albert, Stefan; Schmack, Katharina; Sterzer, Philipp; Schneider, Gaby
2017-11-01
Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM) for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM), which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group differences to
Simulation of nuclear plant operation into a stochastic energy production model
International Nuclear Information System (INIS)
Pacheco, R.L.
1983-04-01
A simulation model of nuclear plant operation is developed to fit into a stochastic energy production model. In order to improve the stochastic model used, and also reduce its computational time burdened by the aggregation of the model of nuclear plant operation, a study of tail truncation of the unsupplied demand distribution function has been performed. (E.G.) [pt
Stochastic modeling of wetland-groundwater systems
Bertassello, Leonardo Enrico; Rao, P. Suresh C.; Park, Jeryang; Jawitz, James W.; Botter, Gianluca
2018-02-01
Modeling and data analyses were used in this study to examine the temporal hydrological variability in geographically isolated wetlands (GIWs), as influenced by hydrologic connectivity to shallow groundwater, wetland bathymetry, and subject to stochastic hydro-climatic forcing. We examined the general case of GIWs coupled to shallow groundwater through exfiltration or infiltration across wetland bottom. We also examined limiting case with the wetland stage as the local expression of the shallow groundwater. We derive analytical expressions for the steady-state probability density functions (pdfs) for wetland water storage and stage using few, scaled, physically-based parameters. In addition, we analyze the hydrologic crossing time properties of wetland stage, and the dependence of the mean hydroperiod on climatic and wetland morphologic attributes. Our analyses show that it is crucial to account for shallow groundwater connectivity to fully understand the hydrologic dynamics in wetlands. The application of the model to two different case studies in Florida, jointly with a detailed sensitivity analysis, allowed us to identify the main drivers of hydrologic dynamics in GIWs under different climate and morphologic conditions.
Stochastic model of radioiodine transport
International Nuclear Information System (INIS)
Schwarz, G.; Hoffman, F.O.
1980-01-01
A research project has been underway at the Oak Ridge National Laboratory with the objective to evaluate dose assessment models and to determine the uncertainty associated with the model predictions. This has resulted in the application of methods to propagate uncertainties through models. Some techniques and results related to this problem are discussed
Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays
Syed Ali, M.; Balasubramaniam, P.
2008-07-01
In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB.
Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays
International Nuclear Information System (INIS)
Syed Ali, M.; Balasubramaniam, P.
2008-01-01
In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB
Stochastic Spectral Descent for Discrete Graphical Models
International Nuclear Information System (INIS)
Carlson, David; Hsieh, Ya-Ping; Collins, Edo; Carin, Lawrence; Cevher, Volkan
2015-01-01
Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.
Brain-inspired Stochastic Models and Implementations
Al-Shedivat, Maruan
2015-05-12
One of the approaches to building artificial intelligence (AI) is to decipher the princi- ples of the brain function and to employ similar mechanisms for solving cognitive tasks, such as visual perception or natural language understanding, using machines. The recent breakthrough, named deep learning, demonstrated that large multi-layer networks of arti- ficial neural-like computing units attain remarkable performance on some of these tasks. Nevertheless, such artificial networks remain to be very loosely inspired by the brain, which rich structures and mechanisms may further suggest new algorithms or even new paradigms of computation. In this thesis, we explore brain-inspired probabilistic mechanisms, such as neural and synaptic stochasticity, in the context of generative models. The two questions we ask here are: (i) what kind of models can describe a neural learning system built of stochastic components? and (ii) how can we implement such systems e ̆ciently? To give specific answers, we consider two well known models and the corresponding neural architectures: the Naive Bayes model implemented with a winner-take-all spiking neural network and the Boltzmann machine implemented in a spiking or non-spiking fashion. We propose and analyze an e ̆cient neuromorphic implementation of the stochastic neu- ral firing mechanism and study the e ̄ects of synaptic unreliability on learning generative energy-based models implemented with neural networks.
Stochastic Modelling of Energy Systems
DEFF Research Database (Denmark)
Andersen, Klaus Kaae
2001-01-01
is that the model structure has to be adequate for practical applications, such as system simulation, fault detection and diagnosis, and design of control strategies. This also reflects on the methods used for identification of the component models. The main result from this research is the identification......In this thesis dynamic models of typical components in Danish heating systems are considered. Emphasis is made on describing and evaluating mathematical methods for identification of such models, and on presentation of component models for practical applications. The thesis consists of seven...... research papers (case studies) together with a summary report. Each case study takes it's starting point in typical heating system components and both, the applied mathematical modelling methods and the application aspects, are considered. The summary report gives an introduction to the scope...
Solvable stochastic dealer models for financial markets
Yamada, Kenta; Takayasu, Hideki; Ito, Takatoshi; Takayasu, Misako
2009-05-01
We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects: the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which have recently been discovered in the study of market price modeling based on random walks.
Modeling and Prediction Using Stochastic Differential Equations
DEFF Research Database (Denmark)
Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp
2016-01-01
Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...
Fuzzy Stochastic Optimization Theory, Models and Applications
Wang, Shuming
2012-01-01
Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzzy random uncertainty. It proceeds in an orderly fashion from the requisite theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization models and their real-life case studies. The volume reflects the fact that randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world, with significant implications in a number of settings. In industrial engineering, management and economics, the chances are high that decision makers will be confronted with information that is simultaneously probabilistically uncertain and fuzzily imprecise, and optimization in the form of a decision must be made in an environment that is doubly uncertain, characterized by a co-occurrence of randomness and fuzziness. This book begins...
Ranking paths in stochastic time-dependent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele D.
2014-01-01
In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in...
Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process
Turner, Douglas C.; Ladde, Gangaram S.
2018-03-01
Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.
Long-time correlations in the stochastic regime
International Nuclear Information System (INIS)
Karney, C.F.F.
1982-11-01
The phase space for Hamiltonians of two degrees of freedom is usually divided into stochastic and integrable components. Even when well into the stochastic regime, integrable orbits may surround small stable regions or islands. The effect of these islands on the correlation function for the stochastic trajectories is examined. Depending on the value of the parameter describing the rotation number for the elliptic fixed point at the center of the island, the long-time correlation function may decay as t -5 or exponentially, but more commonly it decays much more slowly (roughly as t -1 ). As a consequence these small islands may have a profound effect on the properties such as the diffusion coefficient, of the stochastic orbits
Test models for improving filtering with model errors through stochastic parameter estimation
International Nuclear Information System (INIS)
Gershgorin, B.; Harlim, J.; Majda, A.J.
2010-01-01
The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic parameter estimation is developed based on the Stochastic Parameterization Extended Kalman Filter (SPEKF). These new SPEKF-algorithms systematically correct both multiplicative and additive biases and involve exact formulas for propagating the mean and covariance including the parameters in the test model. A comprehensive study is presented of robust parameter regimes for increasing filtering skill through stochastic parameter estimation for turbulent signals as the observation time and observation noise are varied and even when the forcing is incorrectly specified. The results here provide useful guidelines for filtering turbulent signals in more complex systems with significant model errors.
Stochastic resonance in a generalized Von Foerster population growth model
Energy Technology Data Exchange (ETDEWEB)
Lumi, N.; Mankin, R. [Institute of Mathematics and Natural Sciences, Tallinn University, 25 Narva Road, 10120 Tallinn (Estonia)
2014-11-12
The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.
Stochastic Modeling of Past Volcanic Crises
Woo, Gordon
2018-01-01
The statistical foundation of disaster risk analysis is past experience. From a scientific perspective, history is just one realization of what might have happened, given the randomness and chaotic dynamics of Nature. Stochastic analysis of the past is an exploratory exercise in counterfactual history, considering alternative possible scenarios. In particular, the dynamic perturbations that might have transitioned a volcano from an unrest to an eruptive state need to be considered. The stochastic modeling of past volcanic crises leads to estimates of eruption probability that can illuminate historical volcanic crisis decisions. It can also inform future economic risk management decisions in regions where there has been some volcanic unrest, but no actual eruption for at least hundreds of years. Furthermore, the availability of a library of past eruption probabilities would provide benchmark support for estimates of eruption probability in future volcanic crises.
A cavitation model based on Eulerian stochastic fields
Magagnato, F.; Dumond, J.
2013-12-01
Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
A stochastic model for the financial market with discontinuous prices
Directory of Open Access Journals (Sweden)
Leda D. Minkova
1996-01-01
Full Text Available This paper models some situations occurring in the financial market. The asset prices evolve according to a stochastic integral equation driven by a Gaussian martingale. A portfolio process is constrained in such a way that the wealth process covers some obligation. A solution to a linear stochastic integral equation is obtained in a class of cadlag stochastic processes.
Hidden Symmetries of Stochastic Models
Directory of Open Access Journals (Sweden)
Boyka Aneva
2007-05-01
Full Text Available In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.
The Asymptotic Behaviour of a Stochastic 3D LANS-α Model
International Nuclear Information System (INIS)
Caraballo, Tomas; Marquez-Duran, Antonio M.; Real, Jose
2006-01-01
The long-time behaviour of a stochastic 3D LANS-α model on a bounded domain is analysed. First, we reformulate the model as an abstract problem. Next, we establish sufficient conditions ensuring the existence of stationary (steady state) solutions of this abstract nonlinear stochastic evolution equation, and study the stability properties of the model. Finally, we analyse the effects produced by stochastic perturbations in the deterministic version of the system (persistence of exponential stability as well as possible stabilisation effects produced by the noise). The general results are applied to our stochastic LANS-α system throughout the paper
Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power
DEFF Research Database (Denmark)
Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte
2010-01-01
This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...
Modeling stochastic frontier based on vine copulas
Constantino, Michel; Candido, Osvaldo; Tabak, Benjamin M.; da Costa, Reginaldo Brito
2017-11-01
This article models a production function and analyzes the technical efficiency of listed companies in the United States, Germany and England between 2005 and 2012 based on the vine copula approach. Traditional estimates of the stochastic frontier assume that data is multivariate normally distributed and there is no source of asymmetry. The proposed method based on vine copulas allow us to explore different types of asymmetry and multivariate distribution. Using data on product, capital and labor, we measure the relative efficiency of the vine production function and estimate the coefficient used in the stochastic frontier literature for comparison purposes. This production vine copula predicts the value added by firms with given capital and labor in a probabilistic way. It thereby stands in sharp contrast to the production function, where the output of firms is completely deterministic. The results show that, on average, S&P500 companies are more efficient than companies listed in England and Germany, which presented similar average efficiency coefficients. For comparative purposes, the traditional stochastic frontier was estimated and the results showed discrepancies between the coefficients obtained by the application of the two methods, traditional and frontier-vine, opening new paths of non-linear research.
Modelling Evolutionary Algorithms with Stochastic Differential Equations.
Heredia, Jorge Pérez
2017-11-20
There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.
Models of the stochastic activity of neurones
Holden, Arun Vivian
1976-01-01
These notes have grown from a series of seminars given at Leeds between 1972 and 1975. They represent an attempt to gather together the different kinds of model which have been proposed to account for the stochastic activity of neurones, and to provide an introduction to this area of mathematical biology. A striking feature of the electrical activity of the nervous system is that it appears stochastic: this is apparent at all levels of recording, ranging from intracellular recordings to the electroencephalogram. The chapters start with fluctuations in membrane potential, proceed through single unit and synaptic activity and end with the behaviour of large aggregates of neurones: L have chgaen this seque~~e\\/~~';uggest that the interesting behaviourr~f :the nervous system - its individuality, variability and dynamic forms - may in part result from the stochastic behaviour of its components. I would like to thank Dr. Julio Rubio for reading and commenting on the drafts, Mrs. Doris Beighton for producing the fin...
Mathematical models of information and stochastic systems
Kornreich, Philipp
2008-01-01
From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t
Predicting extinction rates in stochastic epidemic models
International Nuclear Information System (INIS)
Schwartz, Ira B; Billings, Lora; Dykman, Mark; Landsman, Alexandra
2009-01-01
We investigate the stochastic extinction processes in a class of epidemic models. Motivated by the process of natural disease extinction in epidemics, we examine the rate of extinction as a function of disease spread. We show that the effective entropic barrier for extinction in a susceptible–infected–susceptible epidemic model displays scaling with the distance to the bifurcation point, with an unusual critical exponent. We make a direct comparison between predictions and numerical simulations. We also consider the effect of non-Gaussian vaccine schedules, and show numerically how the extinction process may be enhanced when the vaccine schedules are Poisson distributed
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik
2009-06-01
The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.
Predicting population extinction or disease outbreaks with stochastic models
Directory of Open Access Journals (Sweden)
Linda J. S. Allen
2017-01-01
Full Text Available Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix.
Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework
International Nuclear Information System (INIS)
Zhou, X.Y.; Li, D.
2000-01-01
This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be 'embedded' into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem
Stochastic Power Control for Time-Varying Long-Term Fading Wireless Networks
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Charalambous Charalambos D
2006-01-01
Full Text Available A new time-varying (TV long-term fading (LTF channel model which captures both the space and time variations of wireless systems is developed. The proposed TV LTF model is based on a stochastic differential equation driven by Brownian motion. This model is more realistic than the static models usually encountered in the literature. It allows viewing the wireless channel as a dynamical system, thus enabling well-developed tools of adaptive and nonadaptive estimation and identification techniques to be applied to this class of problems. In contrast with the traditional models, the statistics of the proposed model are shown to be TV, but converge in steady state to their static counterparts. Moreover, optimal power control algorithms (PCAs based on the new model are proposed. A centralized PCA is shown to reduce to a simple linear programming problem if predictable power control strategies (PPCS are used. In addition, an iterative distributed stochastic PCA is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal-to-interference ratio. Generalizations of the power control problem based on convex optimization techniques are provided if PPCS are not assumed. Numerical results show that there are potentially large gains to be achieved by using TV stochastic models, and the distributed stochastic PCA provides better power stability and consumption than the distributed deterministic PCA.
Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory
Constable, George W. A.; McKane, Alan J.
2017-08-01
The relationship between the M -species stochastic Lotka-Volterra competition (SLVC) model and the M -allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection, and the Moran model with frequency-dependent selection (equivalently a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species' extinction in the SLVC model.
A one-time truncate and encode multiresolution stochastic framework
Energy Technology Data Exchange (ETDEWEB)
Abgrall, R.; Congedo, P.M.; Geraci, G., E-mail: gianluca.geraci@inria.fr
2014-01-15
In this work a novel adaptive strategy for stochastic problems, inspired from the classical Harten's framework, is presented. The proposed algorithm allows building, in a very general manner, stochastic numerical schemes starting from a whatever type of deterministic schemes and handling a large class of problems, from unsteady to discontinuous solutions. Its formulations permits to recover the same results concerning the interpolation theory of the classical multiresolution approach, but with an extension to uncertainty quantification problems. The present strategy permits to build numerical scheme with a higher accuracy with respect to other classical uncertainty quantification techniques, but with a strong reduction of the numerical cost and memory requirements. Moreover, the flexibility of the proposed approach allows to employ any kind of probability density function, even discontinuous and time varying, without introducing further complications in the algorithm. The advantages of the present strategy are demonstrated by performing several numerical problems where different forms of uncertainty distributions are taken into account, such as discontinuous and unsteady custom-defined probability density functions. In addition to algebraic and ordinary differential equations, numerical results for the challenging 1D Kraichnan–Orszag are reported in terms of accuracy and convergence. Finally, a two degree-of-freedom aeroelastic model for a subsonic case is presented. Though quite simple, the model allows recovering some physical key aspect, on the fluid/structure interaction, thanks to the quasi-steady aerodynamic approximation employed. The injection of an uncertainty is chosen in order to obtain a complete parameterization of the mass matrix. All the numerical results are compared with respect to classical Monte Carlo solution and with a non-intrusive Polynomial Chaos method.
Stochastic modeling of the hypothalamic pulse generator activity.
Camproux, A C; Thalabard, J C; Thomas, G
1994-11-01
Luteinizing hormone (LH) is released by the pituitary in discrete pulses. In the monkey, the appearance of LH pulses in the plasma is invariably associated with sharp increases (i.e, volleys) in the frequency of the hypothalamic pulse generator electrical activity, so that continuous monitoring of this activity by telemetry provides a unique means to study the temporal structure of the mechanism generating the pulses. To assess whether the times of occurrence and durations of previous volleys exert significant influence on the timing of the next volley, we used a class of periodic counting process models that specify the stochastic intensity of the process as the product of two factors: 1) a periodic baseline intensity and 2) a stochastic regression function with covariates representing the influence of the past. This approach allows the characterization of circadian modulation and memory range of the process underlying hypothalamic pulse generator activity, as illustrated by fitting the model to experimental data from two ovariectomized rhesus monkeys.
A stochastic model for intermittent search strategies
International Nuclear Information System (INIS)
Benichou, O; Coppey, M; Moreau, M; Suet, P H; Voituriez, R
2005-01-01
It is often necessary, in scientific or everyday life problems, to find a randomly hidden target. What is then the optimal strategy to reach it as rapidly as possible? In this article, we develop a stochastic theory for intermittent search behaviours, which are often observed: the searcher alternates phases of intensive search and slow motion with fast displacements. The first results of this theory have already been announced recently. Here we provide a detailed presentation of the theory, as well as the full derivation of the results. Furthermore, we explicitly discuss the minimization of the time needed to find the target
Stochastic modeling of central apnea events in preterm infants
International Nuclear Information System (INIS)
Clark, Matthew T; Lake, Douglas E; Randall Moorman, J; Delos, John B; Lee, Hoshik; Fairchild, Karen D; Kattwinkel, John
2016-01-01
A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm—stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events—may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge. (paper)
Stochastic modeling of central apnea events in preterm infants.
Clark, Matthew T; Delos, John B; Lake, Douglas E; Lee, Hoshik; Fairchild, Karen D; Kattwinkel, John; Moorman, J Randall
2016-04-01
A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm-stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events-may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
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Shelton Peiris
2017-12-01
Full Text Available This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV components in order to develop the General Long Memory SV (GLMSV model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.
Neural network connectivity and response latency modelled by stochastic processes
DEFF Research Database (Denmark)
Tamborrino, Massimiliano
is connected to thousands of other neurons. The rst question is: how to model neural networks through stochastic processes? A multivariate Ornstein-Uhlenbeck process, obtained as a diffusion approximation of a jump process, is the proposed answer. Obviously, dependencies between neurons imply dependencies......Stochastic processes and their rst passage times have been widely used to describe the membrane potential dynamics of single neurons and to reproduce neuronal spikes, respectively.However, cerebral cortex in human brains is estimated to contain 10-20 billions of neurons and each of them...... between their spike times. Therefore, the second question is: how to detect neural network connectivity from simultaneously recorded spike trains? Answering this question corresponds to investigate the joint distribution of sequences of rst passage times. A non-parametric method based on copulas...
Single-molecule stochastic times in a reversible bimolecular reaction
Keller, Peter; Valleriani, Angelo
2012-08-01
In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.
Stochastic approaches to inflation model building
International Nuclear Information System (INIS)
Ramirez, Erandy; Liddle, Andrew R.
2005-01-01
While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by fundamental physics considerations or by simplicity. An alternative is to generate large numbers of models via a random generation process, such as the flow equations approach. The flow equations approach is known to predict a definite structure to the observational predictions. In this paper, we first demonstrate a more efficient implementation of the flow equations exploiting an analytic solution found by Liddle (2003). We then consider alternative stochastic methods of generating large numbers of inflation models, with the aim of testing whether the structures generated by the flow equations are robust. We find that while typically there remains some concentration of points in the observable plane under the different methods, there is significant variation in the predictions amongst the methods considered
Effects of demographic stochasticity on biological community assembly on evolutionary time scales
Murase, Yohsuke
2010-04-13
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.
Effects of demographic stochasticity on biological community assembly on evolutionary time scales
Murase, Yohsuke; Shimada, Takashi; Ito, Nobuyasu; Rikvold, Per Arne
2010-01-01
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.
Event-Triggered Faults Tolerant Control for Stochastic Systems with Time Delays
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Ling Huang
2016-01-01
Full Text Available This paper is concerned with the state-feedback controller design for stochastic networked control systems (NCSs with random actuator failures and transmission delays. Firstly, an event-triggered scheme is introduced to optimize the performance of the stochastic NCSs. Secondly, stochastic NCSs under event-triggered scheme are modeled as stochastic time-delay systems. Thirdly, some less conservative delay-dependent stability criteria in terms of linear matrix inequalities for the codesign of both the controller gain and the trigger parameters are obtained by using delay-decomposition technique and convex combination approach. Finally, a numerical example is provided to show the less sampled data transmission and less conservatism of the proposed theory.
An extension of clarke's model with stochastic amplitude flip processes
Hoel, Hakon
2014-07-01
Stochastic modeling is an essential tool for studying statistical properties of wireless channels. In multipath fading channel (MFC) models, the signal reception is modeled by a sum of wave path contributions, and Clarke\\'s model is an important example of such which has been widely accepted in many wireless applications. However, since Clarke\\'s model is temporally deterministic, Feng and Field noted that it does not model real wireless channels with time-varying randomness well. Here, we extend Clarke\\'s model to a novel time-varying stochastic MFC model with scatterers randomly flipping on and off. Statistical properties of the MFC model are analyzed and shown to fit well with real signal measurements, and a limit Gaussian process is derived from the model when the number of active wave paths tends to infinity. A second focus of this work is a comparison study of the error and computational cost of generating signal realizations from the MFC model and from its limit Gaussian process. By rigorous analysis and numerical studies, we show that in many settings, signal realizations are generated more efficiently by Gaussian process algorithms than by the MFC model\\'s algorithm. Numerical examples that strengthen these observations are also presented. © 2014 IEEE.
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.
Stochastic population and epidemic models persistence and extinction
Allen, Linda J S
2015-01-01
This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics ...
Stochastic modeling of reinforced concrete structures exposed to chloride attack
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Frier, Christian
2004-01-01
For many reinforced concrete structures corrosion of reinforcement is an important problem since it can result in expensive maintenance and repair actions. Further, a significant reduction of the load-bearing capacity can occur. One mode of corrosion initiation is that the chloride content around...... concentration and reinforcement cover depth are modeled by stochastic fields. The paper contains a description of the parameters to be included in a stochastic model and a proposal for the information needed to obtain values for the parameters in order to be able to perform reliability investigations....... The distribution of the time to initiation of corrosion is estimated by simulation. As an example a bridge pier in a marine environment is considered....
Stochastic Modeling of Reinforced Concrete Structures Exposed to Chloride Attack
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Frier, Christian
2003-01-01
For many reinforced concrete structures corrosion of reinforcement is an important problem since it can result in expensive maintenance and repair actions. Further, a significant reduction of the load-bearing capacity can occur. One mode of corrosion initiation is that the chloride content around...... concentration and reinforcement cover depth are modeled by stochastic fields. The paper contains a description of the parameters to be included in a stochastic model and a proposal for the information needed to obtain values for the parameters in order to be ab le to perform reliability investigations....... The distribution of the time to initiation of corrosion is estimated by simulation. As an example a bridge pier in a marine environment is considered....
Stochastic model of forecasting spare parts demand
Directory of Open Access Journals (Sweden)
Ivan S. Milojević
2012-01-01
Full Text Available If demand is known for the whole planning period (complete information, then this type of demand or a supply system is deterministic. In the simplest cases, the demand per time unit is constant. If demand levels change over time following a precisely determined and pre-known principle, this type of demand is also classified as deterministic. This quality of demand is very rare. In most cases demand is the product of a process, for example TMS maintenance, whose progression cannot be predicted due to a number of factors influencing the process and causing random demand changes. In this case, a supply system must function according to the complete information and with a certain degree of uncertainty. In cases when demand may be defined by some of the laws of the probability theory, we are talking about stochastic demand and a stochastic supply system. Demand can be described by mathematical expectation, mathematical expectation and standard deviation, probability distribution or as a random process. However, there is usually a need for the most complex description, i.e. the complex random process because both intensity of demand and the probability distribution change during the observed intervals. The level of temporal (dynamic series is traditionally considered as a complex phenomenon consisting of four components: - basic tendency of phenomenon development - cyclical impact (long-term, 'ancient' - seasonal effects - random fluctuations. The basic tendency of phenomenon development means a long-term evolution of phenomena. A function that expresses the trajectory of changes of the basic tendency of a phenomenon development in the form of the equation is called a trend. Often, the trend involves time regression; i.e. the coefficients of the proposed functions are often determined by the least squares method. To roughly determine the coefficients of the proposed function, the sum of three and three-point methods are also used. After checking the
Hopf bifurcation of the stochastic model on business cycle
International Nuclear Information System (INIS)
Xu, J; Wang, H; Ge, G
2008-01-01
A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation
Expectation propagation for continuous time stochastic processes
International Nuclear Information System (INIS)
Cseke, Botond; Schnoerr, David; Sanguinetti, Guido; Opper, Manfred
2016-01-01
We consider the inverse problem of reconstructing the posterior measure over the trajectories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference, giving rise to an expectation propagation type algorithm. For non-linear diffusion processes, this is achieved by leveraging moment closure approximations. We then show how the approximation can be extended to a wide class of discrete-state Markov jump processes by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems. (paper)
A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis
Directory of Open Access Journals (Sweden)
Linda J.S. Allen
2017-05-01
Full Text Available Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented. Specifically, models are formulated for continuous-time Markov chains and stochastic differential equations. Some well-known examples are used for illustration such as an SIR epidemic model and a host-vector malaria model. Analytical methods for approximating the probability of a disease outbreak are also discussed. Keywords: Branching process, Continuous-time Markov chain, Minor outbreak, Stochastic differential equation, 2000 MSC: 60H10, 60J28, 92D30
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Stochastic inverse problems: Models and metrics
International Nuclear Information System (INIS)
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-01-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds
Stochastic inverse problems: Models and metrics
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-03-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
Kulasiri, Don
2002-01-01
Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...
Brownian motion model with stochastic parameters for asset prices
Ching, Soo Huei; Hin, Pooi Ah
2013-09-01
The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift μ and volatility σ may change over time. Presently we consider a model in which the parameter x = (μ,σ) is such that its value x (t + Δt) at a short time Δt ahead of the present time t depends on the value of the asset price at time t + Δt as well as the present parameter value x(t) and m-1 other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.
Bayesian inference for hybrid discrete-continuous stochastic kinetic models
International Nuclear Information System (INIS)
Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S
2014-01-01
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)
Stochastic models for surface diffusion of molecules
Energy Technology Data Exchange (ETDEWEB)
Shea, Patrick, E-mail: patrick.shea@dal.ca; Kreuzer, Hans Jürgen [Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)
2014-07-28
We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.
Can Household Benefit from Stochastic Programming Models?
DEFF Research Database (Denmark)
Rasmussen, Kourosh Marjani; Madsen, Claus A.; Poulsen, Rolf
2014-01-01
The Danish mortgage market is large and sophisticated. However, most Danish mortgage banks advise private home-owners based on simple, if sensible, rules of thumb. In recent years a number of papers (from Nielsen and Poulsen in J Econ Dyn Control 28:1267–1289, 2004 over Rasmussen and Zenios in J...... Risk 10:1–18, 2007 to Pedersen et al. in Ann Oper Res, 2013) have suggested a model-based, stochastic programming approach to mortgage choice. This paper gives an empirical comparison of performance over the period 2000–2010 of the rules of thumb to the model-based strategies. While the rules of thumb.......3–0.9 %-points (depending on the borrower’s level of conservatism) compared to the rules of thumb without increasing the risk. The answer to the question in the title is thus affirmative....
International Nuclear Information System (INIS)
Valor, A.; Caleyo, F.; Alfonso, L.; Rivas, D.; Hallen, J.M.
2007-01-01
In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion
Energy Technology Data Exchange (ETDEWEB)
Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 Havana (Cuba); Caleyo, F. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)]. E-mail: fcaleyo@gmail.com; Alfonso, L. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Rivas, D. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Hallen, J.M. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)
2007-02-15
In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion.
Extinction in neutrally stable stochastic Lotka-Volterra models
Dobrinevski, Alexander; Frey, Erwin
2012-05-01
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.
Directory of Open Access Journals (Sweden)
Spiros Pagiatakis
2009-10-01
Full Text Available In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times. It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF. It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at −40 °C, −20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.
El-Diasty, Mohammed; Pagiatakis, Spiros
2009-01-01
In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at -40 °C, -20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.
Stochastic modeling of consumer preferences for health care institutions.
Malhotra, N K
1983-01-01
This paper proposes a stochastic procedure for modeling consumer preferences via LOGIT analysis. First, a simple, non-technical exposition of the use of a stochastic approach in health care marketing is presented. Second, a study illustrating the application of the LOGIT model in assessing consumer preferences for hospitals is given. The paper concludes with several implications of the proposed approach.
A stochastic modeling of recurrent measles epidemic | Kassem ...
African Journals Online (AJOL)
A simple stochastic mathematical model is developed and investigated for the dynamics of measles epidemic. The model, which is a multi-dimensional diffusion process, includes susceptible individuals, latent (exposed), infected and removed individuals. Stochastic effects are assumed to arise in the process of infection of ...
Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson
Directory of Open Access Journals (Sweden)
Bullinger Eric
2006-12-01
Full Text Available Abstract "Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background.
Optimal Stochastic Modeling and Control of Flexible Structures
1988-09-01
1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic
Environmental versus demographic variability in stochastic predator–prey models
International Nuclear Information System (INIS)
Dobramysl, U; Täuber, U C
2013-01-01
In contrast to the neutral population cycles of the deterministic mean-field Lotka–Volterra rate equations, including spatial structure and stochastic noise in models for predator–prey interactions yields complex spatio-temporal structures associated with long-lived erratic population oscillations. Environmental variability in the form of quenched spatial randomness in the predation rates results in more localized activity patches. Our previous study showed that population fluctuations in rare favorable regions in turn cause a remarkable increase in the asymptotic densities of both predators and prey. Very intriguing features are found when variable interaction rates are affixed to individual particles rather than lattice sites. Stochastic dynamics with demographic variability in conjunction with inheritable predation efficiencies generate non-trivial time evolution for the predation rate distributions, yet with overall essentially neutral optimization. (paper)
Approximate models for broken clouds in stochastic radiative transfer theory
International Nuclear Information System (INIS)
Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas
2014-01-01
This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models
Extensions of Statecharts with probability, time, and stochastic timing
Jansen, D.N.
2003-01-01
Statecharts are a graphical language to describe the behaviour of a (computer) system. Statecharts are, among others, used as a part of the UML (Unified Modelling Language). This thesis describes three extensions related to statecharts. One of them is a real-time property language that fits well
SR 97. Alternative models project. Stochastic continuum modelling of Aberg
International Nuclear Information System (INIS)
Widen, H.; Walker, D.
1999-08-01
As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modelling approaches to bedrock performance assessment for a single hypothetical repository, arbitrarily named Aberg. The Aberg repository will adopt input parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The models are restricted to an explicit domain, boundary conditions and canister location to facilitate the comparison. The boundary conditions are based on the regional groundwater model provided in digital format. This study is the application of HYDRASTAR, a stochastic continuum groundwater flow and transport-modelling program. The study uses 34 realisations of 945 canister locations in the hypothetical repository to evaluate the uncertainty of the advective travel time, canister flux (Darcy velocity at a canister) and F-ratio. Several comparisons of variability are constructed between individual canister locations and individual realisations. For the ensemble of all realisations with all canister locations, the study found a median travel time of 27 years, a median canister flux of 7.1 x 10 -4 m/yr and a median F-ratio of 3.3 x 10 5 yr/m. The overall pattern of regional flow is preserved in the site-scale model, as is reflected in flow paths and exit locations. The site-scale model slightly over-predicts the boundary fluxes from the single realisation of the regional model. The explicitly prescribed domain was seen to be slightly restrictive, with 6% of the stream tubes failing to exit the upper surface of the model. Sensitivity analysis and calibration are suggested as possible extensions of the modelling study
Spatial Stochastic Point Models for Reservoir Characterization
Energy Technology Data Exchange (ETDEWEB)
Syversveen, Anne Randi
1997-12-31
The main part of this thesis discusses stochastic modelling of geology in petroleum reservoirs. A marked point model is defined for objects against a background in a two-dimensional vertical cross section of the reservoir. The model handles conditioning on observations from more than one well for each object and contains interaction between objects, and the objects have the correct length distribution when penetrated by wells. The model is developed in a Bayesian setting. The model and the simulation algorithm are demonstrated by means of an example with simulated data. The thesis also deals with object recognition in image analysis, in a Bayesian framework, and with a special type of spatial Cox processes called log-Gaussian Cox processes. In these processes, the logarithm of the intensity function is a Gaussian process. The class of log-Gaussian Cox processes provides flexible models for clustering. The distribution of such a process is completely characterized by the intensity and the pair correlation function of the Cox process. 170 refs., 37 figs., 5 tabs.
Mashhoon, B.
1982-01-01
The influence of a stochastic and isotropic background of gravitational radiation on timing measurements of pulsars is investigated, and it is shown that pulsar timing noise may be used to establish a significant upper limit of about 10 to the -10th on the total energy density of very long-wavelength stochastic gravitational waves. This places restriction on the strength of very long wavelength gravitational waves in the Friedmann model, and such a background is expected to have no significant effect on the approximately 3 K electromagnetic background radiation or on the dynamics of a cluster of galaxies.
STOCHASTIC MODELING OF COMPRESSIVE STRENGTH OF PHOSPHORUS SLAG CONTENT CEMENT
Directory of Open Access Journals (Sweden)
Ali Allahverdi
2016-07-01
Full Text Available One of the common methods for quick determination of compressive strength as one of the most important properties for assessment of cement quality is to apply various modeling approaches. This study is aimed at finding a model for estimating the compressive strength of phosphorus slag content cements. For this purpose, the compressive strengths of chemically activated high phosphorus slag content cement prepared from phosphorus slag (80 wt.%, Portland cement (14 wt.% and a compound chemical activator containing sodium sulfate and anhydrite (6 wt.% were measured at various Blaine finenesses and curing times. Based on the obtained results, a primary stochastic model in terms of curing time and Blaine fineness has been developed. Then, another different dataset was used to incorporate composition variable including weight fractions of phosphorus slag, cement, and activator in the model. This model can be effectively used to predict the compressive strength of phosphorus slag content cements at various Blaine finenesses, curing times, and compositions.
Stochastic series expansion simulation of the t -V model
Wang, Lei; Liu, Ye-Hua; Troyer, Matthias
2016-04-01
We present an algorithm for the efficient simulation of the half-filled spinless t -V model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless t -V model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.
ARMA modelling of neutron stochastic processes with large measurement noise
International Nuclear Information System (INIS)
Zavaljevski, N.; Kostic, Lj.; Pesic, M.
1994-01-01
An autoregressive moving average (ARMA) model of the neutron fluctuations with large measurement noise is derived from langevin stochastic equations and validated using time series data obtained during prompt neutron decay constant measurements at the zero power reactor RB in Vinca. Model parameters are estimated using the maximum likelihood (ML) off-line algorithm and an adaptive pole estimation algorithm based on the recursive prediction error method (RPE). The results show that subcriticality can be determined from real data with high measurement noise using much shorter statistical sample than in standard methods. (author)
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
Gay-Balmaz, François; Holm, Darryl D.
2018-01-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
Gay-Balmaz, François; Holm, Darryl D.
2018-06-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Approximation of itô integrals arising in stochastic time-delayed systems
Bagchi, Arunabha
1984-01-01
Likelihood functional for stochastic linear time-delayed systems involve Itô integrals with respect to the observed data. Since the Wiener process appearing in the standard observation process model for such systems is not realizable and the physically observed process is smooth, one needs to study
Bicriterion a priori route choice in stochastic time-dependent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele
In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path...
Bicriterion a priori route choice in stochastic time-dependent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Pretolani, D; Andersen, K A
2006-01-01
In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path...
Stochastic growth logistic model with aftereffect for batch fermentation process
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-06-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
Stochastic growth logistic model with aftereffect for batch fermentation process
International Nuclear Information System (INIS)
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-01-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits
Stochastic growth logistic model with aftereffect for batch fermentation process
Energy Technology Data Exchange (ETDEWEB)
Rosli, Norhayati; Ayoubi, Tawfiqullah [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah; Rahman, Haliza Abdul [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Salleh, Madihah Md [Department of Biotechnology Industry, Faculty of Biosciences and Bioengineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2014-06-19
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time
Dhar, Amrit
2017-01-01
Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780
A stochastic model for early placental development.
Cotter, Simon L
2014-08-01
In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational-age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely understood and are difficult to study in vivo. In this paper, we model the early development of the human placenta, based on the hypothesis that this is driven by a chemoattractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that disruption of spiral arteries can exert profound effects on placental shape, particularly if this is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, predisposing to pregnancy complications. Through statistical analysis of model placentas, we are able to characterize the probability that a given placenta grew in a disrupted environment, and even able to distinguish between different disruptions.
Stochastic modelling of two-phase flows including phase change
International Nuclear Information System (INIS)
Hurisse, O.; Minier, J.P.
2011-01-01
Stochastic modelling has already been developed and applied for single-phase flows and incompressible two-phase flows. In this article, we propose an extension of this modelling approach to two-phase flows including phase change (e.g. for steam-water flows). Two aspects are emphasised: a stochastic model accounting for phase transition and a modelling constraint which arises from volume conservation. To illustrate the whole approach, some remarks are eventually proposed for two-fluid models. (authors)
Survival Analysis of a Nonautonomous Logistic Model with Stochastic Perturbation
Directory of Open Access Journals (Sweden)
Chun Lu
2012-01-01
Full Text Available Taking white noise into account, a stochastic nonautonomous logistic model is proposed and investigated. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence, and global asymptotic stability are established. Moreover, the threshold between weak persistence and extinction is obtained. Finally, we introduce some numerical simulink graphics to illustrate our main results.
Analysis and reconstruction of stochastic coupled map lattice models
International Nuclear Information System (INIS)
Coca, Daniel; Billings, Stephen A.
2003-01-01
The Letter introduces a general stochastic coupled lattice map model together with an algorithm to estimate the nodal equations involved based only on a small set of observable variables and in the presence of stochastic perturbations. More general forms of the Frobenius-Perron and the transfer operators, which describe the evolution of densities under the action of the CML transformation, are derived
Quantum dynamical time evolutions as stochastic flows on phase space
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Guerra, F.; Sirigue, M.; Sirigue-Collin, M.
1984-01-01
We are mainly interested in describing the time development of the Wigner functions by means of stochastic processes. In the second section we recall the main properties of the Wigner functions as well as those of their Fourier transform. In the next one we derive the evolution equation of these functions for a class of Hamiltonians and we give a probabilistic expression for the solution of these equations by means of a stochastic flow in phase space which reminds of the classical flows. In the last section we remark that the previously defined flow can be extended to the bounded continuous functions on phase space and that this flow conserves the cone generated by the Wigner functions. (orig./HSI)
Stochastic lag time in nucleated linear self-assembly
Energy Technology Data Exchange (ETDEWEB)
Tiwari, Nitin S. [Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Schoot, Paul van der [Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2016-06-21
Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerization reactions. One of the most important characteristic features in this kind of problem is the existence of a lag phase before self-assembly takes off, which is what we focus attention on. We study the associated lag time as a function of system size and kinetic pathway. We find that the leading order stochastic contribution to the lag time before polymerization commences is inversely proportional to the system volume for large-enough system size for all nine reaction pathways tested. Finite-size corrections to this do depend on the kinetic pathway.
Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model
Directory of Open Access Journals (Sweden)
Michael Schultz
2018-03-01
Full Text Available Efficient boarding procedures have to consider both operational constraints and the individual passenger behavior. In contrast to the aircraft handling processes of fueling, catering and cleaning, the boarding process is more driven by passengers than by airport or airline operators. This paper delivers a comprehensive set of operational data including classification of boarding times, passenger arrival times, times to store hand luggage, and passenger interactions in the aircraft cabin as a reliable basis for calibrating models for aircraft boarding. In this paper, a microscopic approach is used to model the passenger behavior, where the passenger movement is defined as a one-dimensional, stochastic, and time/space discrete transition process. This model is used to compare measurements from field trials of boarding procedures with simulation results and demonstrates a deviation smaller than 5%.
A probabilistic graphical model based stochastic input model construction
International Nuclear Information System (INIS)
Wan, Jiang; Zabaras, Nicholas
2014-01-01
Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media
Stochastic modeling of virus capsid assembly pathways
Schwartz, Russell
2009-03-01
Virus capsids have become a key model system for understanding self-assembly due to their high complexity, robust and efficient assembly processes, and experimental tractability. Our ability to directly examine and manipulate capsid assembly kinetics in detail nonetheless remains limited, creating a need for computer models that can infer experimentally inaccessible features of the assembly process and explore the effects of hypothetical manipulations on assembly trajectories. We have developed novel algorithms for stochastic simulation of capsid assembly [1,2] that allow us to model capsid assembly over broad parameter spaces [3]. We apply these methods to study the nature of assembly pathway control in virus capsids as well as their sensitivity to assembly conditions and possible experimental interventions. [4pt] [1] F. Jamalyaria, R. Rohlfs, and R. Schwartz. J Comp Phys 204, 100 (2005). [0pt] [2] N. Misra and R. Schwartz. J Chem Phys 129, in press (2008). [0pt] [3] B. Sweeney, T. Zhang, and R. Schwartz. Biophys J 94, 772 (2008).
Systematic parameter inference in stochastic mesoscopic modeling
Energy Technology Data Exchange (ETDEWEB)
Lei, Huan; Yang, Xiu [Pacific Northwest National Laboratory, Richland, WA 99352 (United States); Li, Zhen [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)
2017-02-01
We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are “sparse”. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.
Two new algorithms to combine kriging with stochastic modelling
Venema, Victor; Lindau, Ralf; Varnai, Tamas; Simmer, Clemens
2010-05-01
Two main groups of statistical methods used in the Earth sciences are geostatistics and stochastic modelling. Geostatistical methods, such as various kriging algorithms, aim at estimating the mean value for every point as well as possible. In case of sparse measurements, such fields have less variability at small scales and a narrower distribution as the true field. This can lead to biases if a nonlinear process is simulated driven by such a kriged field. Stochastic modelling aims at reproducing the statistical structure of the data in space and time. One of the stochastic modelling methods, the so-called surrogate data approach, replicates the value distribution and power spectrum of a certain data set. While stochastic methods reproduce the statistical properties of the data, the location of the measurement is not considered. This requires the use of so-called constrained stochastic models. Because radiative transfer through clouds is a highly nonlinear process, it is essential to model the distribution (e.g. of optical depth, extinction, liquid water content or liquid water path) accurately. In addition, the correlations within the cloud field are important, especially because of horizontal photon transport. This explains the success of surrogate cloud fields for use in 3D radiative transfer studies. Up to now, however, we could only achieve good results for the radiative properties averaged over the field, but not for a radiation measurement located at a certain position. Therefore we have developed a new algorithm that combines the accuracy of stochastic (surrogate) modelling with the positioning capabilities of kriging. In this way, we can automatically profit from the large geostatistical literature and software. This algorithm is similar to the standard iterative amplitude adjusted Fourier transform (IAAFT) algorithm, but has an additional iterative step in which the surrogate field is nudged towards the kriged field. The nudging strength is gradually
A Simple, Realistic Stochastic Model of Gastric Emptying.
Directory of Open Access Journals (Sweden)
Jiraphat Yokrattanasak
Full Text Available Several models of Gastric Emptying (GE have been employed in the past to represent the rate of delivery of stomach contents to the duodenum and jejunum. These models have all used a deterministic form (algebraic equations or ordinary differential equations, considering GE as a continuous, smooth process in time. However, GE is known to occur as a sequence of spurts, irregular both in size and in timing. Hence, we formulate a simple stochastic process model, able to represent the irregular decrements of gastric contents after a meal. The model is calibrated on existing literature data and provides consistent predictions of the observed variability in the emptying trajectories. This approach may be useful in metabolic modeling, since it describes well and explains the apparently heterogeneous GE experimental results in situations where common gastric mechanics across subjects would be expected.
The stochastic resonance for the incidence function model of metapopulation
Li, Jiang-Cheng; Dong, Zhi-Wei; Zhou, Ruo-Wei; Li, Yun-Xian; Qian, Zhen-Wei
2017-06-01
A stochastic model with endogenous and exogenous periodicities is proposed in this paper on the basis of metapopulation dynamics to model the crop yield losses due to pests and diseases. The rationale is that crop yield losses occur because the physiology of the growing crop is negatively affected by pests and diseases in a dynamic way over time as crop both grows and develops. Metapopulation dynamics can thus be used to model the resultant crop yield losses. The stochastic metapopulation process is described by using the Simplified Incidence Function model (IFM). Compared to the original IFMs, endogenous and exogenous periodicities are considered in the proposed model to handle the cyclical patterns observed in pest infestations, diseases epidemics, and exogenous affecting factors such as temperature and rainfalls. Agricultural loss data in China are used to fit the proposed model. Experimental results demonstrate that: (1) Model with endogenous and exogenous periodicities is a better fit; (2) When the internal system fluctuations and external environmental fluctuations are negatively correlated, EIL or the cost of loss is monotonically increasing; when the internal system fluctuations and external environmental fluctuations are positively correlated, an outbreak of pests and diseases might occur; (3) If the internal system fluctuations and external environmental fluctuations are positively correlated, an optimal patch size can be identified which will greatly weaken the effects of external environmental influence and hence inhibit pest infestations and disease epidemics.
Adaptive control of chaotic systems with stochastic time varying unknown parameters
Energy Technology Data Exchange (ETDEWEB)
Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu
2008-10-15
In this paper based on the Lyapunov stability theorem, an adaptive control scheme is proposed for stabilizing the unstable periodic orbits (UPO) of chaotic systems. It is assumed that the chaotic system has some linearly dependent unknown parameters which are stochastically time varying. The stochastic parameters are modeled through the Weiner process derivative. To demonstrate the effectiveness of the proposed technique it has been applied to the Lorenz, Chen and Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in stabilizing the UPO of chaotic systems in noisy environment.
Insights into pre-reversal paleosecular variation from stochastic models
Directory of Open Access Journals (Sweden)
Klaudio ePeqini
2015-09-01
Full Text Available To provide insights on the paleosecular variation of the geomagnetic field and the mechanism of reversals, long time series of the dipolar magnetic moment are generated by two different stochastic models, known as the domino model and the inhomogeneous Lebovitz disk dynamo model, with initial values taken from the from paleomagnetic data. The former model considers mutual interactions of N macrospins embedded in a uniformly rotating medium, where random forcing and dissipation act on each macrospin. With an appropriate set of the model’s parameters values, the series generated by this model have similar statistical behaviour to the time series of the SHA.DIF.14K model. The latter model is an extension of the classical two-disk Rikitake model, considering N dynamo elements with appropriate interactions between them.We varied the parameters set of both models aiming at generating suitable time series with behaviour similar to the long time series of recent secular variation (SV. Such series are then extended to the near future, obtaining reversals in both cases of models. The analysis of the time series generated by simulating the models show that the reversals appears after a persistent period of low intensity geomagnetic field, as it is occurring in the present times.
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
Prediction of interest rate using CKLS model with stochastic parameters
International Nuclear Information System (INIS)
Ying, Khor Chia; Hin, Pooi Ah
2014-01-01
The Chan, Karolyi, Longstaff and Sanders (CKLS) model is a popular one-factor model for describing the spot interest rates. In this paper, the four parameters in the CKLS model are regarded as stochastic. The parameter vector φ (j) of four parameters at the (J+n)-th time point is estimated by the j-th window which is defined as the set consisting of the observed interest rates at the j′-th time point where j≤j′≤j+n. To model the variation of φ (j) , we assume that φ (j) depends on φ (j−m) , φ (j−m+1) ,…, φ (j−1) and the interest rate r j+n at the (j+n)-th time point via a four-dimensional conditional distribution which is derived from a [4(m+1)+1]-dimensional power-normal distribution. Treating the (j+n)-th time point as the present time point, we find a prediction interval for the future value r j+n+1 of the interest rate at the next time point when the value r j+n of the interest rate is given. From the above four-dimensional conditional distribution, we also find a prediction interval for the future interest rate r j+n+d at the next d-th (d≥2) time point. The prediction intervals based on the CKLS model with stochastic parameters are found to have better ability of covering the observed future interest rates when compared with those based on the model with fixed parameters
Prediction of interest rate using CKLS model with stochastic parameters
Energy Technology Data Exchange (ETDEWEB)
Ying, Khor Chia [Faculty of Computing and Informatics, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor (Malaysia); Hin, Pooi Ah [Sunway University Business School, No. 5, Jalan Universiti, Bandar Sunway, 47500 Subang Jaya, Selangor (Malaysia)
2014-06-19
The Chan, Karolyi, Longstaff and Sanders (CKLS) model is a popular one-factor model for describing the spot interest rates. In this paper, the four parameters in the CKLS model are regarded as stochastic. The parameter vector φ{sup (j)} of four parameters at the (J+n)-th time point is estimated by the j-th window which is defined as the set consisting of the observed interest rates at the j′-th time point where j≤j′≤j+n. To model the variation of φ{sup (j)}, we assume that φ{sup (j)} depends on φ{sup (j−m)}, φ{sup (j−m+1)},…, φ{sup (j−1)} and the interest rate r{sub j+n} at the (j+n)-th time point via a four-dimensional conditional distribution which is derived from a [4(m+1)+1]-dimensional power-normal distribution. Treating the (j+n)-th time point as the present time point, we find a prediction interval for the future value r{sub j+n+1} of the interest rate at the next time point when the value r{sub j+n} of the interest rate is given. From the above four-dimensional conditional distribution, we also find a prediction interval for the future interest rate r{sub j+n+d} at the next d-th (d≥2) time point. The prediction intervals based on the CKLS model with stochastic parameters are found to have better ability of covering the observed future interest rates when compared with those based on the model with fixed parameters.
Uncertainty modelling of atmospheric dispersion by stochastic ...
Indian Academy of Sciences (India)
by stochastic response surface method under aleatory ... 3Health Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India e-mail: ...... Brandimarte P 2011 Quantitative methods: An introduction for business management.
Infinite time interval backward stochastic differential equations with continuous coefficients.
Zong, Zhaojun; Hu, Feng
2016-01-01
In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).
Stochastic modelling of avascular tumour growth and therapy
International Nuclear Information System (INIS)
Sahoo, S; Sahoo, A; Shearer, S F C
2011-01-01
In this paper, a generalized stochastic model for the growth of avascular tumours is presented. This model captures the dynamical evolution of avascular tumour cell subpopulations by incorporating Gaussian white noise into the growth rate of the mitotic function. This work generalizes the deterministic model proposed by Sherratt and Chaplain (2001 J. Math. Biol. 43 291) where they formulated a tumour model in an in vivo setting, in terms of continuum densities of proliferating, quiescent and necrotic cells. Detailed simulations of our model show that the inclusion of Gaussian noise in the original model of Sherratt and Chaplain substantially distorts the overall structure of the density profiles in addition to reducing the speed of tumour growth. Within this stochastic carcinogenesis framework the action of therapy is also investigated by replacing Gaussian white noise with a therapy term. We compare a constant therapy protocol with a logarithmic time-dependent protocol. Our results predict that a logarithmic therapy is more effective than the constant therapy protocol.
Stochastic models for predicting environmental impact in aquatic ecosystems
International Nuclear Information System (INIS)
Stewart-Oaten, A.
1986-01-01
The purpose of stochastic predictions are discussed in relation to the environmental impacts of nuclear power plants on aquatic ecosystems. One purpose is to aid in making rational decisions about whether a power plant should be built, where, and how it should be designed. The other purpose is to check on the models themselves in the light of what eventually happens. The author discusses the role or statistical decision theory in the decision-making problem. Various types of stochastic models and their problems are presented. In addition some suggestions are made for generating usable stochastic models, and checking and improving on them. 12 references
Stochastic models of edge turbulent transport in the thermonuclear reactors
International Nuclear Information System (INIS)
Volchenkov, Dima
2005-01-01
Two-dimensional stochastic model of turbulent transport in the scrape-off layer (SOL) of thermonuclear reactors is considered. Convective instability arisen in the system with respect to perturbations reveals itself in the strong outward bursts of particle density propagating ballistically across the SOL. The criterion of stability for the fluctuations of particle density is formulated. A possibility to stabilize the system depends upon the certain type of plasma waves interactions and the certain scenario of turbulence. A bias of limiter surface would provide a fairly good insulation of chamber walls excepting for the resonant cases. Pdf of the particle flux for the large magnitudes of flux events is modeled with a simple discrete time toy model of I-dimensional random walks concluding at the boundary. The spectra of wandering times feature the pdf of particle flux in the model and qualitatively reproduce the experimental statistics of transport events
Stochastic Watershed Models for Risk Based Decision Making
Vogel, R. M.
2017-12-01
Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation
Model selection for integrated pest management with stochasticity.
Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel
2018-04-07
In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model. Copyright © 2017 Elsevier Ltd. All rights reserved.
Modeling stochasticity and robustness in gene regulatory networks.
Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis
2009-06-15
Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.
International Nuclear Information System (INIS)
Nikzad, Mehdi; Mozafari, Babak; Bashirvand, Mahdi; Solaymani, Soodabeh; Ranjbar, Ali Mohamad
2012-01-01
Recently in electricity markets, a massive focus has been made on setting up opportunities for participating demand side. Such opportunities, also known as demand response (DR) options, are triggered by either a grid reliability problem or high electricity prices. Two important challenges that market operators are facing are appropriate designing and reasonable pricing of DR options. In this paper, time-of-use program (TOU) as a prevalent time-varying program is modeled linearly based on own and cross elasticity definition. In order to decide on TOU rates, a stochastic model is proposed in which the optimum TOU rates are determined based on grid reliability index set by the operator. Expected Load Not Supplied (ELNS) is used to evaluate reliability of the power system in each hour. The proposed stochastic model is formulated as a two-stage stochastic mixed-integer linear programming (SMILP) problem and solved using CPLEX solver. The validity of the method is tested over the IEEE 24-bus test system. In this regard, the impact of the proposed pricing method on system load profile; operational costs and required capacity of up- and down-spinning reserve as well as improvement of load factor is demonstrated. Also the sensitivity of the results to elasticity coefficients is investigated. -- Highlights: ► Time-of-use demand response program is linearly modeled. ► A stochastic model is proposed to determine the optimum TOU rates based on ELNS index set by the operator. ► The model is formulated as a short-term two-stage stochastic mixed-integer linear programming problem.
Estimation of stochastic volatility by using Ornstein-Uhlenbeck type models
Mariani, Maria C.; Bhuiyan, Md Al Masum; Tweneboah, Osei K.
2018-02-01
In this study, we develop a technique for estimating the stochastic volatility (SV) of a financial time series by using Ornstein-Uhlenbeck type models. Using the daily closing prices from developed and emergent stock markets, we conclude that the incorporation of stochastic volatility into the time varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. Furthermore, our estimation algorithm is feasible with large data sets and have good convergence properties.
On changes of measure in stochastic volatility models
Directory of Open Access Journals (Sweden)
Bernard Wong
2006-01-01
models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.
Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates
Jiang, G.J.; van der Sluis, P.J.
2000-01-01
This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the
Development of the Stochastic Lung Model for Asthma
International Nuclear Information System (INIS)
Dobos, E.; Borbely-Kiss, I.; Kertesz, Zs.; Balashazy, I.
2005-01-01
Complete text of publication follows. The Stochastic Lung Model is a state-of-the-art tool for the investigation of the health impact of atmospheric aerosols. This model has already been tested and applied to calculate the deposition fractions of aerosols in different regions of the human respiratory tract. The health effects of inhaled aerosols may strongly depend on the distribution of deposition within the respiratory tract. In the current study three Asthma Models have been incorporated into the Stochastic Lung Deposition Code. A common new feature of these models is that the breathing cycle may be asymmetric. It means that the inspiration time, the expiration time and the two breath hold times are independent. And the code can simulate the mucus blockage, too. The main characteristics of the models are the followings: a) ASTHMA MODEL I: One input bronchial asthma factor is applied for the whole tracheobronchial region. The code multiplies all tracheobroncial diameters with this single value. b) ASTHMA MODEL II: Bronchial asthma factors have to be given for each bronchial generation as input data (21 values). The program multiplies the diameter of bronchi with these factors. c) ASTHMA MODEL III: Here, only the range of bronchial asthma factors are presented as input data and the code selects randomly the exact factors in pre-described airway generations. In this case the stochastic character appears in the Asthma Model, as well. As an example, Figure 1 shows the deposition fractions in the tracheobronchial and acinar regions of the human lung in the case of healthy and asthmatic adults at sitting breathing conditions as a function of particle size computed by Asthma Model I where the bronchial asthma factor was 30%. These models have been tested and compared for different types of asthma at various breathing conditions and in a wide range of particle sizes. The distribution of deposition in the characteristic regions of the respiratory tract have been computed
Stochastic Modeling and Performance Analysis of Multimedia SoCs
DEFF Research Database (Denmark)
Raman, Balaji; Nouri, Ayoub; Gangadharan, Deepak
2013-01-01
solutions where each modeling technique has both the above mentioned characteristics. We present a probabilistic analytical framework and a statistical model checking approach to design system-on-chips for low-cost multimedia systems. We apply the modeling techniques to size the output buffer in a video......Reliability and flexibility are among the key required features of a framework used to model a system. Existing approaches to design resource-constrained, soft-real time systems either provide guarantees for output quality or account for loss in the system, but not both. We propose two independent...... decoder. The results shows that, for our stochastic design metric, the analytical framework upper bounds (and relatively accurate) compare to the statistical model checking technique. Also, we observed significant reduction in resource usage (such as output buffer size) with tolerable loss in output...
Some Remarks on Stochastic Versions of the Ramsey Growth Model
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2012-01-01
Roč. 19, č. 29 (2012), s. 139-152 ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/10/0956; GA ČR GAP402/11/0150 Institutional support: RVO:67985556 Keywords : Economic dynamics * Ramsey growth model with disturbance * stochastic dynamic programming * multistage stochastic programs Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/sladky-some remarks on stochastic versions of the ramsey growth model.pdf
Stochastic Modeling and Analysis of Power System with Renewable Generation
DEFF Research Database (Denmark)
Chen, Peiyuan
Unlike traditional fossil-fuel based power generation, renewable generation such as wind power relies on uncontrollable prime sources such as wind speed. Wind speed varies stochastically, which to a large extent determines the stochastic behavior of power generation from wind farms...... that such a stochastic model can be used to simulate the effect of load management on the load duration curve. As CHP units are turned on and off by regulating power, CHP generation has discrete output and thus can be modeled by a transition matrix based discrete Markov chain. As the CHP generation has a strong diurnal...
Time Series, Stochastic Processes and Completeness of Quantum Theory
International Nuclear Information System (INIS)
Kupczynski, Marian
2011-01-01
Most of physical experiments are usually described as repeated measurements of some random variables. Experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared with the probabilities provided by the algorithms of quantum theory (QT). In spite of statistical predictions of QT a claim was made that it provided the most complete description of the data and of the underlying physical phenomena. This claim could be easily rejected if some fine structures, averaged out in the standard descriptive statistical analysis, were found in time series of experimental data. To search for these structures one has to use more subtle statistical tools which were developed to study time series produced by various stochastic processes. In this talk we review some of these tools. As an example we show how the standard descriptive statistical analysis of the data is unable to reveal a fine structure in a simulated sample of AR (2) stochastic process. We emphasize once again that the violation of Bell inequalities gives no information on the completeness or the non locality of QT. The appropriate way to test the completeness of quantum theory is to search for fine structures in time series of the experimental data by means of the purity tests or by studying the autocorrelation and partial autocorrelation functions.
STOCHASTIC MODELING OF INFLATION IN NIGERIA
African Journals Online (AJOL)
2006-04-04
Apr 4, 2006 ... In this paper, we adopt a time series approach in modeling inflation in ... KEYWORDS: Buys-Ballot table; Quadratic trend; Seasonal multiplicative model, ..... Basic Statistics for Business and Economics, 2nd ed, Irwin, USA.
GPU Computing in Bayesian Inference of Realized Stochastic Volatility Model
International Nuclear Information System (INIS)
Takaishi, Tetsuya
2015-01-01
The realized stochastic volatility (RSV) model that utilizes the realized volatility as additional information has been proposed to infer volatility of financial time series. We consider the Bayesian inference of the RSV model by the Hybrid Monte Carlo (HMC) algorithm. The HMC algorithm can be parallelized and thus performed on the GPU for speedup. The GPU code is developed with CUDA Fortran. We compare the computational time in performing the HMC algorithm on GPU (GTX 760) and CPU (Intel i7-4770 3.4GHz) and find that the GPU can be up to 17 times faster than the CPU. We also code the program with OpenACC and find that appropriate coding can achieve the similar speedup with CUDA Fortran
Beam life-time with intrabeam scattering and stochastic cooling
International Nuclear Information System (INIS)
Wei, J.; Ruggiero, A.G.
1991-01-01
A transport equation has been derived in terms of the longitudinal action variable to describe the time evolution of the longitudinal density distribution of a bunched hadron beam in the presence of intrabeam scattering and stochastic cooling. A computer program has been developed to numerically solve this equation. Both beam loss and bunch-shape evolution have been investigated for the 197 Au 79+ beams during the 10-hour storage in the Relativistic Heavy Ion Collider currently under construction at the Brookhaven National Laboratory. 9 refs., 1 fig
Stochastic process corrosion growth models for pipeline reliability
International Nuclear Information System (INIS)
Bazán, Felipe Alexander Vargas; Beck, André Teófilo
2013-01-01
Highlights: •Novel non-linear stochastic process corrosion growth model is proposed. •Corrosion rate modeled as random Poisson pulses. •Time to corrosion initiation and inherent time-variability properly represented. •Continuous corrosion growth histories obtained. •Model is shown to precisely fit actual corrosion data at two time points. -- Abstract: Linear random variable corrosion models are extensively employed in reliability analysis of pipelines. However, linear models grossly neglect well-known characteristics of the corrosion process. Herein, a non-linear model is proposed, where corrosion rate is represented as a Poisson square wave process. The resulting model represents inherent time-variability of corrosion growth, produces continuous growth and leads to mean growth at less-than-one power of time. Different corrosion models are adjusted to the same set of actual corrosion data for two inspections. The proposed non-linear random process corrosion growth model leads to the best fit to the data, while better representing problem physics
Stochastic Greybox Modeling for Control of an Alternating Activated Sludge Process
DEFF Research Database (Denmark)
Halvgaard, Rasmus Fogtmann; Vezzaro, Luca; Grum, M.
We present a stochastic greybox model of a BioDenitro WWTP that can be used for short time horizon Model Predictive Control. The model is based on a simpliﬁed ASM1 model and takes model uncertainty in to account. It estimates unmeasured state variables in the system, e.g. the inlet concentration...
Stochastic quantization of geometrodynamic curved space-time
International Nuclear Information System (INIS)
Prugovecki, E.
1981-01-01
It is proposed that quantum rather than classical test particles be used in recent operational definitions of space-time. In the resulting quantum space-time the role of test particle trajectories is taken over by propagators. The introduced co-ordinate values are stochastic rather than deterministic, the afore-mentioned propagators providing probability amplitudes describing fluctuations of measured co-ordinates around their mean values. It is shown that, if a geometrodynamic point of view based on 3 + 1 foliations of space-time is adopted, self-consistent families of propagators for quantum test particles in free fall can be constructed. The resulting formalism for quantum space-time is outlined and the quantization of spatially flat Robertson-Walker space-times is provided as an illustration. (author)
Evapotranspiration Estimates for a Stochastic Soil-Moisture Model
Chaleeraktrakoon, Chavalit; Somsakun, Somrit
2009-03-01
Potential evapotranspiration is information that is necessary for applying a widely used stochastic model of soil moisture (I. Rodriguez Iturbe, A. Porporato, L. Ridolfi, V. Isham and D. R. Cox, Probabilistic modelling of water balance at a point: The role of climate, soil and vegetation, Proc. Roy. Soc. London A455 (1999) 3789-3805). An objective of the present paper is thus to find a proper estimate of the evapotranspiration for the stochastic model. This estimate is obtained by comparing the calculated soil-moisture distribution resulting from various techniques, such as Thornthwaite, Makkink, Jensen-Haise, FAO Modified Penman, and Blaney-Criddle, with an observed one. The comparison results using five sequences of daily soil-moisture for a dry season from November 2003 to April 2004 (Udornthani Province, Thailand) have indicated that all methods can be used if the weather information required is available. This is because their soil-moisture distributions are alike. In addition, the model is shown to have its ability in approximately describing the phenomenon at a weekly or biweekly time scale which is desirable for agricultural engineering applications.
Volatility Degree Forecasting of Stock Market by Stochastic Time Strength Neural Network
Directory of Open Access Journals (Sweden)
Haiyan Mo
2013-01-01
Full Text Available In view of the applications of artificial neural networks in economic and financial forecasting, a stochastic time strength function is introduced in the backpropagation neural network model to predict the fluctuations of stock price changes. In this model, stochastic time strength function gives a weight for each historical datum and makes the model have the effect of random movement, and then we investigate and forecast the behavior of volatility degrees of returns for the Chinese stock market indexes and some global market indexes. The empirical research is performed in testing the prediction effect of SSE, SZSE, HSI, DJIA, IXIC, and S&P 500 with different selected volatility degrees in the established model.
Stochastic higher spin six vertex model and Macdonald measures
Borodin, Alexei
2018-02-01
We prove an identity that relates the q-Laplace transform of the height function of a (higher spin inhomogeneous) stochastic six vertex model in a quadrant on one side and a multiplicative functional of a Macdonald measure on the other. The identity is used to prove the GUE Tracy-Widom asymptotics for two instances of the stochastic six vertex model via asymptotic analysis of the corresponding Schur measures.
Bridging time scales in cellular decision making with a stochastic bistable switch
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Waldherr Steffen
2010-08-01
Full Text Available Abstract Background Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. Some of these transformations act over a very long time scale on the cell population level, up to the entire lifespan of the organism. Results In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Conclusions Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.
Stochastic Landau equation with time-dependent drift
International Nuclear Information System (INIS)
Swift, J.B.; Hohenberg, P.C.; Ahlers, G.
1991-01-01
The stochastic differential equation τ 0 ∂ tA =ε(t)A-g 3 A 3 +bar f(t), where bar f(t) is Gaussian white noise, is studied for arbitrary time dependence of ε(t). In particular, cases are considered where ε(t) goes through the bifurcation of the deterministic system, which occurs at ε=0. In the limit of weak noise an approximate analytic expression generalizing earlier work of Suzuki [Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) Suppl. 64, 402 (1978)] is obtained for the time-dependent distribution function P(A,t). The results compare favorably with a numerical simulation of the stochastic equation for the case of a linear ramp (both increasing and decreasing) and for a periodic time dependence of ε(t). The procedure can be generalized to an arbitrary deterministic part ∂ tA =D(A,t)+bar f(t), but the deterministic equation may then have to be solved numerically
Directory of Open Access Journals (Sweden)
Xueling Jiang
2014-01-01
Full Text Available The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and the M-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.
Computational stochastic model of ions implantation
Energy Technology Data Exchange (ETDEWEB)
Zmievskaya, Galina I., E-mail: zmi@gmail.ru; Bondareva, Anna L., E-mail: bal310775@yandex.ru [M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation); Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru [VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation); Maino, Giuseppe, E-mail: giuseppe.maino@enea.it [Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)
2015-03-10
Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.
Detecting stochastic backgrounds of gravitational waves with pulsar timing arrays
Siemens, Xavier
2016-03-01
For the past decade the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has been using the Green Bank Telescope and the Arecibo Observatory to monitor millisecond pulsars. NANOGrav, along with two other international collaborations, the European Pulsar Timing Array and the Parkes Pulsar Timing Array in Australia, form a consortium of consortia: the International Pulsar Timing Array (IPTA). The goal of the IPTA is to directly detect low-frequency gravitational waves which cause small changes to the times of arrival of radio pulses from millisecond pulsars. In this talk I will discuss the work of NANOGrav and the IPTA, as well as our sensitivity to stochastic backgrounds of gravitational waves. I will show that a detection of the background produced by supermassive black hole binaries is possible by the end of the decade. Supported by the NANOGrav Physics Frontiers Center.
Study on individual stochastic model of GNSS observations for precise kinematic applications
Próchniewicz, Dominik; Szpunar, Ryszard
2015-04-01
The proper definition of mathematical positioning model, which is defined by functional and stochastic models, is a prerequisite to obtain the optimal estimation of unknown parameters. Especially important in this definition is realistic modelling of stochastic properties of observations, which are more receiver-dependent and time-varying than deterministic relationships. This is particularly true with respect to precise kinematic applications which are characterized by weakening model strength. In this case, incorrect or simplified definition of stochastic model causes that the performance of ambiguity resolution and accuracy of position estimation can be limited. In this study we investigate the methods of describing the measurement noise of GNSS observations and its impact to derive precise kinematic positioning model. In particular stochastic modelling of individual components of the variance-covariance matrix of observation noise performed using observations from a very short baseline and laboratory GNSS signal generator, is analyzed. Experimental test results indicate that the utilizing the individual stochastic model of observations including elevation dependency and cross-correlation instead of assumption that raw measurements are independent with the same variance improves the performance of ambiguity resolution as well as rover positioning accuracy. This shows that the proposed stochastic assessment method could be a important part in complex calibration procedure of GNSS equipment.
Energy Technology Data Exchange (ETDEWEB)
Lutaif, N.A. [Departamento de Clínica Médica, Faculdade de Ciências Médicas, Universidade Estadual de Campinas, Campinas, SP (Brazil); Palazzo, R. Jr [Departamento de Telemática, Faculdade de Engenharia Elétrica e Computação, Universidade Estadual de Campinas, Campinas, SP (Brazil); Gontijo, J.A.R. [Departamento de Clínica Médica, Faculdade de Ciências Médicas, Universidade Estadual de Campinas, Campinas, SP (Brazil)
2014-01-17
Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile.
International Nuclear Information System (INIS)
Lutaif, N.A.; Palazzo, R. Jr; Gontijo, J.A.R.
2014-01-01
Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile
Yang, Xin; Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan
2016-01-01
This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems.
Composed particle model in stochastic electrodynamics
International Nuclear Information System (INIS)
Brunini, S.A.
1985-01-01
We analyse the statistical properties of the non-relativistic motion of a particle that has two constituents having finite nasses and charges. The main interaction is in contact with thermal and zero point radiation of Stochastic Electrodynamics. (M.W.O.) [pt
International Nuclear Information System (INIS)
Granita; Bahar, A.
2015-01-01
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)
2015-03-09
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.
Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate
Directory of Open Access Journals (Sweden)
Chaoqun Xu
2013-01-01
Full Text Available We present a stochastic simple chemostat model in which the dilution rate was influenced by white noise. The long time behavior of the system is studied. Mainly, we show how the solution spirals around the washout equilibrium and the positive equilibrium of deterministic system under different conditions. Furthermore, the sufficient conditions for persistence in the mean of the stochastic system and washout of the microorganism are obtained. Numerical simulations are carried out to support our results.
Modelling the heat dynamics of a building using stochastic differential equations
DEFF Research Database (Denmark)
Andersen, Klaus Kaae; Madsen, Henrik; Hansen, Lars Henrik
2000-01-01
estimation and model validation, while physical knowledge is used in forming the model structure. The suggested lumped parameter model is thus based on thermodynamics and formulated as a system of stochastic differential equations. Due to the continuous time formulation the parameters of the model...
Developing a new stochastic competitive model regarding inventory and price
Rashid, Reza; Bozorgi-Amiri, Ali; Seyedhoseini, S. M.
2015-09-01
Within the competition in today's business environment, the design of supply chains becomes more complex than before. This paper deals with the retailer's location problem when customers choose their vendors, and inventory costs have been considered for retailers. In a competitive location problem, price and location of facilities affect demands of customers; consequently, simultaneous optimization of the location and inventory system is needed. To prepare a realistic model, demand and lead time have been assumed as stochastic parameters, and queuing theory has been used to develop a comprehensive mathematical model. Due to complexity of the problem, a branch and bound algorithm has been developed, and its performance has been validated in several numerical examples, which indicated effectiveness of the algorithm. Also, a real case has been prepared to demonstrate performance of the model for real world.
Directory of Open Access Journals (Sweden)
Elston Timothy C
2004-03-01
Full Text Available Abstract Background Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. Results We have developed the software package Biochemical Network Stochastic Simulator (BioNetS for efficientlyand accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solvesthe appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. Conclusions We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.
Multivariate moment closure techniques for stochastic kinetic models
International Nuclear Information System (INIS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-01-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs
Multivariate moment closure techniques for stochastic kinetic models
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
A complementarity model for solving stochastic natural gas market equilibria
International Nuclear Information System (INIS)
Zhuang Jifang; Gabriel, Steven A.
2008-01-01
This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems
Tsunamis: stochastic models of occurrence and generation mechanisms
Geist, Eric L.; Oglesby, David D.
2014-01-01
The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.
A complementarity model for solving stochastic natural gas market equilibria
International Nuclear Information System (INIS)
Jifang Zhuang; Gabriel, S.A.
2008-01-01
This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems. (author)
Parameter estimation in stochastic rainfall-runoff models
DEFF Research Database (Denmark)
Jonsdottir, Harpa; Madsen, Henrik; Palsson, Olafur Petur
2006-01-01
A parameter estimation method for stochastic rainfall-runoff models is presented. The model considered in the paper is a conceptual stochastic model, formulated in continuous-discrete state space form. The model is small and a fully automatic optimization is, therefore, possible for estimating all...... the parameter values are optimal for simulation or prediction. The data originates from Iceland and the model is designed for Icelandic conditions, including a snow routine for mountainous areas. The model demands only two input data series, precipitation and temperature and one output data series...
Analysis of dynamic regimes in stochastically forced Kaldor model
International Nuclear Information System (INIS)
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-01-01
We consider the business cycle Kaldor model forced by random noise. Detailed parametric analysis of deterministic system is carried out and zones of coexisting stable equilibrium and stable limit cycle are found. Noise-induced transitions between these attractors are studied using stochastic sensitivity function technique and confidence domains method. Critical values of noise intensity corresponding to noise-induced transitions “equilibrium → cycle” and “cycle → equilibrium” are estimated. Dominants in combined stochastic regimes are discussed.
A stochastic analysis for a phytoplankton-zooplankton model
International Nuclear Information System (INIS)
Ge, G; Wang, H-L; Xu, J
2008-01-01
A simple phytoplankton-zooplankton nonlinear dynamical model was proposed to study the coexistence of all the species and a Hopf bifurcation was observed. In order to study the effect of environmental robustness on this system, we have stochastically perturbed the system with respect to white noise around its positive interior equilibrium. We have observed that the system remains stochastically stable around the positive equilibrium for same parametric values in the deterministic situation
Earthquake occurrence as stochastic event: (1) theoretical models
Energy Technology Data Exchange (ETDEWEB)
Basili, A.; Basili, M.; Cagnetti, V.; Colombino, A.; Jorio, V.M.; Mosiello, R.; Norelli, F.; Pacilio, N.; Polinari, D.
1977-01-01
The present article intends liaisoning the stochastic approach in the description of earthquake processes suggested by Lomnitz with the experimental evidence reached by Schenkova that the time distribution of some earthquake occurrence is better described by a Negative Bionomial distribution than by a Poisson distribution. The final purpose of the stochastic approach might be a kind of new way for labeling a given area in terms of seismic risk.
Outbreak and Extinction Dynamics in a Stochastic Ebola Model
Nieddu, Garrett; Bianco, Simone; Billings, Lora; Forgoston, Eric; Kaufman, James
A zoonotic disease is a disease that can be passed between animals and humans. In many cases zoonotic diseases can persist in the animal population even if there are no infections in the human population. In this case we call the infected animal population the reservoir for the disease. Ebola virus disease (EVD) and SARS are both notable examples of such diseases. There is little work devoted to understanding stochastic disease extinction and reintroduction in the presence of a reservoir. Here we build a stochastic model for EVD and explicitly consider the presence of an animal reservoir. Using a master equation approach and a WKB ansatz, we determine the associated Hamiltonian of the system. Hamilton's equations are then used to numerically compute the 12-dimensional optimal path to extinction, which is then used to estimate mean extinction times. We also numerically investigate the behavior of the model for dynamic population size. Our results provide an improved understanding of outbreak and extinction dynamics in diseases like EVD.
Maximum likelihood approach for several stochastic volatility models
International Nuclear Information System (INIS)
Camprodon, Jordi; Perelló, Josep
2012-01-01
Volatility measures the amplitude of price fluctuations. Despite it being one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility follow a two-dimensional diffusion process where volatility is the stochastic diffusion coefficient of the log-price dynamics. We apply this method to the simplest versions of the expOU, the OU and the Heston stochastic volatility models and we study their performance in terms of the log-price probability, the volatility probability, and its Mean First-Passage Time. The approach has some predictive power on the future returns amplitude by only knowing the current volatility. The assumed models do not consider long-range volatility autocorrelation and the asymmetric return-volatility cross-correlation but the method still yields very naturally these two important stylized facts. We apply the method to different market indices and with a good performance in all cases. (paper)
Analysis of stochastic effects in Kaldor-type business cycle discrete model
Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna
2016-07-01
We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.
The multivariate supOU stochastic volatility model
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Stelzer, Robert
Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order...... structure of the volatility, the log returns, as well as their "squares" are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations....... In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach....
Fixation and escape times in stochastic game learning
International Nuclear Information System (INIS)
Realpe-Gomez, John; Szczesny, Bartosz; Galla, Tobias; Dall’Asta, Luca
2012-01-01
Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning processes in a simple 2×2 game, for two-player games with cyclic interaction, and in the context of the best-shot network game. The analogues of finite populations in evolution are here finite batches of observations between strategy updates. We study when and how such fixation can occur, and present results on the average time-to-fixation from numerical simulations. Simple cases are also amenable to analytical approaches and we provide estimates of the behaviour of so-called escape times as a function of the batch size. The differences and similarities with escape and fixation in evolutionary dynamics are discussed. (paper)
Introduction to stochastic models in biology
DEFF Research Database (Denmark)
Ditlevsen, Susanne; Samson, Adeline
2013-01-01
This chapter is concerned with continuous time processes, which are often modeled as a system of ordinary differential equations (ODEs). These models assume that the observed dynamics are driven exclusively by internal, deterministic mechanisms. However, real biological systems will always be exp...
Liu, Xiangdong; Li, Qingze; Pan, Jianxin
2018-06-01
Modern medical studies show that chemotherapy can help most cancer patients, especially for those diagnosed early, to stabilize their disease conditions from months to years, which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs. In order to better understand the dynamics of tumor-immune responses under chemotherapy, deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper. The basic dynamical properties, such as boundedness, existence and stability of equilibrium points, are investigated in the deterministic model. Extended stochastic models include stochastic differential equations (SDEs) model and continuous-time Markov chain (CTMC) model, which accounts for the variability in cellular reproduction, growth and death, interspecific competitions, and immune response to chemotherapy. The CTMC model is harnessed to estimate the extinction probability of tumor cells. Numerical simulations are performed, which confirms the obtained theoretical results.
Stochastic models to simulate paratuberculosis in dairy herds
DEFF Research Database (Denmark)
Nielsen, Søren Saxmose; Weber, M.F.; Kudahl, Anne Margrethe Braad
2011-01-01
Stochastic simulation models are widely accepted as a means of assessing the impact of changes in daily management and the control of different diseases, such as paratuberculosis, in dairy herds. This paper summarises and discusses the assumptions of four stochastic simulation models and their use...... the models are somewhat different in their underlying principles and do put slightly different values on the different strategies, their overall findings are similar. Therefore, simulation models may be useful in planning paratuberculosis strategies in dairy herds, although as with all models caution...
Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations
Christensen, H. M.; Dawson, A.; Palmer, T.
2017-12-01
Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.
On stochastic modeling of the modernized global positioning system (GPS) L2C signal
International Nuclear Information System (INIS)
Elsobeiey, Mohamed; El-Rabbany, Ahmed
2010-01-01
In order to take full advantage of the modernized GPS L2C signal, it is essential that its stochastic characteristics and code bias be rigorously determined. In this paper, long sessions of GPS measurements are used to study the stochastic characteristics of the modernized GPS L2C signal. As a byproduct, the stochastic characteristics of the legacy GPS signals, namely C/A and P2 codes, are also determined, which are used to verify the developed stochastic model of the modernized signal. The differential code biases between P2 and C2, DCB P2-C2 , are also estimated using the Bernese GPS software. It is shown that the developed models improved the precise point positioning (PPP) solution and convergence time
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
A theory of Markovian time-inconsistent stochastic control in discrete time
DEFF Research Database (Denmark)
Bjork, Tomas; Murgoci, Agatha
2014-01-01
We develop a theory for a general class of discrete-time stochastic control problems that, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We attack these problems by viewing them within a game theoretic framework, and we look for subgame...
Setting development goals using stochastic dynamical system models.
Ranganathan, Shyam; Nicolis, Stamatios C; Bali Swain, Ranjula; Sumpter, David J T
2017-01-01
The Millennium Development Goals (MDG) programme was an ambitious attempt to encourage a globalised solution to important but often-overlooked development problems. The programme led to wide-ranging development but it has also been criticised for unrealistic and arbitrary targets. In this paper, we show how country-specific development targets can be set using stochastic, dynamical system models built from historical data. In particular, we show that the MDG target of two-thirds reduction of child mortality from 1990 levels was infeasible for most countries, especially in sub-Saharan Africa. At the same time, the MDG targets were not ambitious enough for fast-developing countries such as Brazil and China. We suggest that model-based setting of country-specific targets is essential for the success of global development programmes such as the Sustainable Development Goals (SDG). This approach should provide clear, quantifiable targets for policymakers.
Stochastic motion of a particle in a model fluctuating medium
International Nuclear Information System (INIS)
Moreau, M.; Gaveau, B.; Perera, A.; Frankowicz, M.
1993-01-01
We present several models of time fluctuating media with finite memory, consisting in one and two-dimensional lattices, the Modes of which fluctuate between two internal states according to a Poisson process. A particle moves on the lattice, the diffusion by the Modes depending on their internal state. Such models can be used for the microscopic theory of reaction constants in a dense phase, or for the study of diffusion or reactivity in a complex medium. In a number of cases, the transmission probability of the medium is computed exactly; it is shown that stochastic resonances can occur, an optimal transmission being obtained for a convenient choice of parameters. In more general situations, approximate solutions are given in the case of short and moderate memory of the obstacles. The diffusion in an infinite two-dimensional lattice is studied, and the memory is shown to affect the distribution of the particles rather than the diffusion law. (author). 25 refs, 5 figs
On the stochastic dynamics of disordered spin models
International Nuclear Information System (INIS)
Semerjian, G.; Montanari, A.; Cugliandolo, L.F.
2003-09-01
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in equilibrium with a thermal bath. We propose a fluctuation principle that allows us to derive fluctuation-dissipation relations for many-time correlations and linear responses. We also speculate on how these features will be modified in systems evolving slowly out of equilibrium, as finite-dimensional or dilute spin-glasses. Secondly, we present a formalism that allows one to derive a series of approximated equations that determine the dynamics of disordered spin models on random (hyper) graphs. (author)
Liu, Hongjian; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.
2016-07-01
This paper deals with the robust H∞ state estimation problem for a class of memristive recurrent neural networks with stochastic time-delays. The stochastic time-delays under consideration are governed by a Bernoulli-distributed stochastic sequence. The purpose of the addressed problem is to design the robust state estimator such that the dynamics of the estimation error is exponentially stable in the mean square, and the prescribed ? performance constraint is met. By utilizing the difference inclusion theory and choosing a proper Lyapunov-Krasovskii functional, the existence condition of the desired estimator is derived. Based on it, the explicit expression of the estimator gain is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is employed to demonstrate the effectiveness and applicability of the proposed estimation approach.
Electricity Market Stochastic Dynamic Model and Its Mean Stability Analysis
Directory of Open Access Journals (Sweden)
Zhanhui Lu
2014-01-01
Full Text Available Based on the deterministic dynamic model of electricity market proposed by Alvarado, a stochastic electricity market model, considering the random nature of demand sides, is presented in this paper on the assumption that generator cost function and consumer utility function are quadratic functions. The stochastic electricity market model is a generalization of the deterministic dynamic model. Using the theory of stochastic differential equations, stochastic process theory, and eigenvalue techniques, the determining conditions of the mean stability for this electricity market model under small Gauss type random excitation are provided and testified theoretically. That is, if the demand elasticity of suppliers is nonnegative and the demand elasticity of consumers is negative, then the stochastic electricity market model is mean stable. It implies that the stability can be judged directly by initial data without any computation. Taking deterministic electricity market data combined with small Gauss type random excitation as numerical samples to interpret random phenomena from a statistical perspective, the results indicate the conclusions above are correct, valid, and practical.
Stochastic approach to pitting-corrosion-extreme modelling in low-carbon steel
Energy Technology Data Exchange (ETDEWEB)
Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado 10400, La Habana (Cuba); Caleyo, F. [Departamento de Ingenieria Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Rivas, D.; Hallen, J.M. [Departamento de Ingenieria Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)
2010-03-15
A stochastic model previously developed by the authors using Markov chains has been improved in the light of new experimental evidence. The new model has been successfully applied to reproduce the time evolution of extreme pitting corrosion depths in low-carbon steel. The model is shown to provide a better physical understanding of the pitting process.
Optimisation of timetable-based, stochastic transit assignment models based on MSA
DEFF Research Database (Denmark)
Nielsen, Otto Anker; Frederiksen, Rasmus Dyhr
2006-01-01
(CRM), such a large-scale transit assignment model was developed and estimated. The Stochastic User Equilibrium problem was solved by the Method of Successive Averages (MSA). However, the model suffered from very large calculation times. The paper focuses on how to optimise transit assignment models...
Stochastic approach to pitting-corrosion-extreme modelling in low-carbon steel
International Nuclear Information System (INIS)
Valor, A.; Caleyo, F.; Rivas, D.; Hallen, J.M.
2010-01-01
A stochastic model previously developed by the authors using Markov chains has been improved in the light of new experimental evidence. The new model has been successfully applied to reproduce the time evolution of extreme pitting corrosion depths in low-carbon steel. The model is shown to provide a better physical understanding of the pitting process.
Dynamic stochastic accumulation model with application to pension savings management
Directory of Open Access Journals (Sweden)
Melicherčik Igor
2010-01-01
Full Text Available We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross model. The optimal decision as a solution to the corresponding dynamic stochastic program is a function of the duration of saving, the level of savings and the short rate. Qualitative and quantitative properties of the optimal solution are analyzed. The model is tested on the funded pillar of the Slovak pension system. The results are calculated for various risk preferences of a saver.
Methods and models in mathematical biology deterministic and stochastic approaches
Müller, Johannes
2015-01-01
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Stochastic description of heterogeneities of permeability within groundwater flow models
International Nuclear Information System (INIS)
Cacas, M.C.; Lachassagne, P.; Ledoux, E.; Marsily, G. de
1991-01-01
In order to model radionuclide migration in the geosphere realistically at the field scale, the hydrogeologist needs to be able to simulate groundwater flow in heterogeneous media. Heterogeneity of the medium can be described using a stochastic approach, that affects the way in which a flow model is formulated. In this paper, we discuss the problems that we have encountered in modelling both continuous and fractured media. The stochastic approach leads to a methodology that enables local measurements of permeability to be integrated into a model which gives a good prediction of groundwater flow on a regional scale. 5 Figs.; 8 Refs
Real-Time Demand Side Management Algorithm Using Stochastic Optimization
Directory of Open Access Journals (Sweden)
Moses Amoasi Acquah
2018-05-01
Full Text Available A demand side management technique is deployed along with battery energy-storage systems (BESS to lower the electricity cost by mitigating the peak load of a building. Most of the existing methods rely on manual operation of the BESS, or even an elaborate building energy-management system resorting to a deterministic method that is susceptible to unforeseen growth in demand. In this study, we propose a real-time optimal operating strategy for BESS based on density demand forecast and stochastic optimization. This method takes into consideration uncertainties in demand when accounting for an optimal BESS schedule, making it robust compared to the deterministic case. The proposed method is verified and tested against existing algorithms. Data obtained from a real site in South Korea is used for verification and testing. The results show that the proposed method is effective, even for the cases where the forecasted demand deviates from the observed demand.
A decision dependent stochastic process model for repairable systems with applications
Directory of Open Access Journals (Sweden)
Paul F. Zantek
2015-12-01
This paper mathematically formalizes the notion of how management actions impact the functioning of a repairable system over time by developing a new stochastic process model for such systems. The proposed model is illustrated using both simulated and real data. The proposed model compares favorably to other models for well-known data on Boeing airplanes. The model is further illustrated and compared to other models on failure time and maintenance data stemming from the South Texas Project nuclear power plant.
The Ising Decision Maker: a binary stochastic network for choice response time.
Verdonck, Stijn; Tuerlinckx, Francis
2014-07-01
The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (c) 2014 APA, all rights reserved.
Lipan, Ovidiu; Ferwerda, Cameron
2018-02-01
The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.
Quasi-continuous stochastic simulation framework for flood modelling
Moustakis, Yiannis; Kossieris, Panagiotis; Tsoukalas, Ioannis; Efstratiadis, Andreas
2017-04-01
Typically, flood modelling in the context of everyday engineering practices is addressed through event-based deterministic tools, e.g., the well-known SCS-CN method. A major shortcoming of such approaches is the ignorance of uncertainty, which is associated with the variability of soil moisture conditions and the variability of rainfall during the storm event.In event-based modeling, the sole expression of uncertainty is the return period of the design storm, which is assumed to represent the acceptable risk of all output quantities (flood volume, peak discharge, etc.). On the other hand, the varying antecedent soil moisture conditions across the basin are represented by means of scenarios (e.g., the three AMC types by SCS),while the temporal distribution of rainfall is represented through standard deterministic patterns (e.g., the alternative blocks method). In order to address these major inconsistencies,simultaneously preserving the simplicity and parsimony of the SCS-CN method, we have developed a quasi-continuous stochastic simulation approach, comprising the following steps: (1) generation of synthetic daily rainfall time series; (2) update of potential maximum soil moisture retention, on the basis of accumulated five-day rainfall; (3) estimation of daily runoff through the SCS-CN formula, using as inputs the daily rainfall and the updated value of soil moisture retention;(4) selection of extreme events and application of the standard SCS-CN procedure for each specific event, on the basis of synthetic rainfall.This scheme requires the use of two stochastic modelling components, namely the CastaliaR model, for the generation of synthetic daily data, and the HyetosMinute model, for the disaggregation of daily rainfall to finer temporal scales. Outcomes of this approach are a large number of synthetic flood events, allowing for expressing the design variables in statistical terms and thus properly evaluating the flood risk.
Stochastic modeling of a serial killer.
Simkin, M V; Roychowdhury, V P
2014-08-21
We analyze the time pattern of the activity of a serial killer, who during 12 years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of "Devil's staircase" type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We illustrate analytical results by numerical simulation. Time pattern activity data from two other serial killers further substantiate our analysis. Copyright © 2014 Elsevier Ltd. All rights reserved.
A comparison of the stochastic and machine learning approaches in hydrologic time series forecasting
Kim, T.; Joo, K.; Seo, J.; Heo, J. H.
2016-12-01
Hydrologic time series forecasting is an essential task in water resources management and it becomes more difficult due to the complexity of runoff process. Traditional stochastic models such as ARIMA family has been used as a standard approach in time series modeling and forecasting of hydrological variables. Due to the nonlinearity in hydrologic time series data, machine learning approaches has been studied with the advantage of discovering relevant features in a nonlinear relation among variables. This study aims to compare the predictability between the traditional stochastic model and the machine learning approach. Seasonal ARIMA model was used as the traditional time series model, and Random Forest model which consists of decision tree and ensemble method using multiple predictor approach was applied as the machine learning approach. In the application, monthly inflow data from 1986 to 2015 of Chungju dam in South Korea were used for modeling and forecasting. In order to evaluate the performances of the used models, one step ahead and multi-step ahead forecasting was applied. Root mean squared error and mean absolute error of two models were compared.
Epigenetics and Evolution: Transposons and the Stochastic Epigenetic Modification Model
Directory of Open Access Journals (Sweden)
Sergio Branciamore
2015-04-01
Full Text Available In addition to genetic variation, epigenetic variation and transposons can greatly affect the evolutionary fitnesses landscape and gene expression. Previously we proposed a mathematical treatment of a general epigenetic variation model that we called Stochastic Epigenetic Modification (SEM model. In this study we follow up with a special case, the Transposon Silencing Model (TSM, with, once again, emphasis on quantitative treatment. We have investigated the evolutionary effects of epigenetic changes due to transposon (T insertions; in particular, we have considered a typical gene locus A and postulated that (i the expression level of gene A depends on the epigenetic state (active or inactive of a cis- located transposon element T, (ii stochastic variability in the epigenetic silencing of T occurs only in a short window of opportunity during development, (iii the epigenetic state is then stable during further development, and (iv the epigenetic memory is fully reset at each generation. We develop the model using two complementary approaches: a standard analytical population genetics framework (di usion equations and Monte-Carlo simulations. Both approaches led to similar estimates for the probability of fixation and time of fixation of locus TA with initial frequency P in a randomly mating diploid population of effective size Ne. We have ascertained the e ect that ρ, the probability of transposon Modification during the developmental window, has on the population (species. One of our principal conclusions is that as ρ increases, the pattern of fixation of the combined TA locus goes from "neutral" to "dominant" to "over-dominant". We observe that, under realistic values of ρ, epigenetic Modifications can provide an e cient mechanism for more rapid fixation of transposons and cis-located gene alleles. The results obtained suggest that epigenetic silencing, even if strictly transient (being reset at each generation, can still have signi cant
Stochastic dynamic modeling of regular and slow earthquakes
Aso, N.; Ando, R.; Ide, S.
2017-12-01
Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal
On a Versatile Stochastic Growth Model
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Samiur Arif
2012-06-01
Full Text Available Growth phenomena are ubiquitous and pervasive not only in biology and the medical sciences, but also in economics, marketing and the computer and social sciences. We introduce a three-parameter version of the classic pure-birth process growth model when suitably instantiated, can be used to model growth phenomena in many seemingly unrelated application domains. We point out that the model is computationally attractive since it admits of conceptually simple, closed form solutions for the time-dependent probabilities.
Qualitative and Quantitative Integrated Modeling for Stochastic Simulation and Optimization
Directory of Open Access Journals (Sweden)
Xuefeng Yan
2013-01-01
Full Text Available The simulation and optimization of an actual physics system are usually constructed based on the stochastic models, which have both qualitative and quantitative characteristics inherently. Most modeling specifications and frameworks find it difficult to describe the qualitative model directly. In order to deal with the expert knowledge, uncertain reasoning, and other qualitative information, a qualitative and quantitative combined modeling specification was proposed based on a hierarchical model structure framework. The new modeling approach is based on a hierarchical model structure which includes the meta-meta model, the meta-model and the high-level model. A description logic system is defined for formal definition and verification of the new modeling specification. A stochastic defense simulation was developed to illustrate how to model the system and optimize the result. The result shows that the proposed method can describe the complex system more comprehensively, and the survival probability of the target is higher by introducing qualitative models into quantitative simulation.
Stochastic analysis of epidemics on adaptive time varying networks
Kotnis, Bhushan; Kuri, Joy
2013-06-01
Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an “adaptive threshold,” i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.
Eco-reliable path finding in time-variant and stochastic networks
International Nuclear Information System (INIS)
Li, Wenjie; Yang, Lixing; Wang, Li; Zhou, Xuesong; Liu, Ronghui; Gao, Ziyou
2017-01-01
This paper addresses a route guidance problem for finding the most eco-reliable path in time-variant and stochastic networks such that travelers can arrive at the destination with the maximum on-time probability while meeting vehicle emission standards imposed by government regulators. To characterize the dynamics and randomness of transportation networks, the link travel times and emissions are assumed to be time-variant random variables correlated over the entire network. A 0–1 integer mathematical programming model is formulated to minimize the probability of late arrival by simultaneously considering the least expected emission constraint. Using the Lagrangian relaxation approach, the primal model is relaxed into a dualized model which is further decomposed into two simple sub-problems. A sub-gradient method is developed to reduce gaps between upper and lower bounds. Three sets of numerical experiments are tested to demonstrate the efficiency and performance of our proposed model and algorithm. - Highlights: • The most eco-reliable path is defined in time-variant and stochastic networks. • The model is developed with on-time arrival probability and emission constraints. • The sub-gradient and label correcting algorithm are integrated to solve the model. • Numerical experiments demonstrate the effectiveness of developed approaches.
Probabilistic Forecast of Wind Power Generation by Stochastic Differential Equation Models
Elkantassi, Soumaya
2017-04-01
Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.
The critical domain size of stochastic population models.
Reimer, Jody R; Bonsall, Michael B; Maini, Philip K
2017-02-01
Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.
Effects of time delay on stochastic resonance of the stock prices in financial system
International Nuclear Information System (INIS)
Li, Jiang-Cheng; Li, Chun; Mei, Dong-Cheng
2014-01-01
The effect of time delay on stochastic resonance of the stock prices in finance system was investigated. The time delay is introduced into the Heston model driven by the extrinsic and intrinsic periodic information for stock price. The signal power amplification (SPA) was calculated by numerical simulation. The results indicate that an optimal critical value of delay time maximally enhances the reverse-resonance in the behaviors of SPA as a function of long-run variance of volatility or cross correlation coefficient between noises for both cases of intrinsic and extrinsic periodic information. Moreover, in both cases, being a critical value in the delay time, when the delay time takes value below the critical value, reverse-resonance increases with the delay time increasing, however, when the delay time takes value above the critical value, the reverse-resonance decrease with the delay time increasing. - Highlights: • The effects of delay time on stochastic resonance of the stock prices was investigated. • There is an optimal critical value of delay time maximally enhances the reverse-resonance • The reverse-resonance increases with the delay time increasing as the delay time takes value below the critical value • The reverse-resonance decrease with the delay time increasing as the delay time takes value above the critical value
Effects of time delay on stochastic resonance of the stock prices in financial system
Energy Technology Data Exchange (ETDEWEB)
Li, Jiang-Cheng [Department of Physics, Yunnan University, Kunming, 650091 (China); Li, Chun [Department of Computer Science, Puer Teachers' College, Puer 665000 (China); Mei, Dong-Cheng, E-mail: meidch@ynu.edu.cn [Department of Physics, Yunnan University, Kunming, 650091 (China)
2014-06-13
The effect of time delay on stochastic resonance of the stock prices in finance system was investigated. The time delay is introduced into the Heston model driven by the extrinsic and intrinsic periodic information for stock price. The signal power amplification (SPA) was calculated by numerical simulation. The results indicate that an optimal critical value of delay time maximally enhances the reverse-resonance in the behaviors of SPA as a function of long-run variance of volatility or cross correlation coefficient between noises for both cases of intrinsic and extrinsic periodic information. Moreover, in both cases, being a critical value in the delay time, when the delay time takes value below the critical value, reverse-resonance increases with the delay time increasing, however, when the delay time takes value above the critical value, the reverse-resonance decrease with the delay time increasing. - Highlights: • The effects of delay time on stochastic resonance of the stock prices was investigated. • There is an optimal critical value of delay time maximally enhances the reverse-resonance • The reverse-resonance increases with the delay time increasing as the delay time takes value below the critical value • The reverse-resonance decrease with the delay time increasing as the delay time takes value above the critical value.
Czech Academy of Sciences Publication Activity Database
Šolc, Milan
2002-01-01
Roč. 216, 07 (2002), s. 869-893 ISSN 0942-9352 R&D Projects: GA AV ČR IAA4032101 Institutional research plan: CEZ:AV0Z4032918 Keywords : stochastic kinetics * fluctuation * first-passage time Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 0.854, year: 2002
A Simulation-Based Dynamic Stochastic Route Choice Model for Evacuation
Directory of Open Access Journals (Sweden)
Xing Zhao
2012-01-01
Full Text Available This paper establishes a dynamic stochastic route choice model for evacuation to simulate the propagation process of traffic flow and estimate the stochastic route choice under evacuation situations. The model contains a lane-group-based cell transmission model (CTM which sets different traffic capacities for links with different turning movements to flow out in an evacuation situation, an actual impedance model which is to obtain the impedance of each route in time units at each time interval and a stochastic route choice model according to the probit-based stochastic user equilibrium. In this model, vehicles loading at each origin at each time interval are assumed to choose an evacuation route under determinate road network, signal design, and OD demand. As a case study, the proposed model is validated on the network nearby Nanjing Olympic Center after the opening ceremony of the 10th National Games of the People's Republic of China. The traffic volumes and clearing time at five exit points of the evacuation zone are calculated by the model to compare with survey data. The results show that this model can appropriately simulate the dynamic route choice and evolution process of the traffic flow on the network in an evacuation situation.
Herath, Narmada; Del Vecchio, Domitilla
2018-03-01
Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.
Stochastic processes analysis in nuclear reactor using ARMA models
International Nuclear Information System (INIS)
Zavaljevski, N.
1990-01-01
The analysis of ARMA model derived from general stochastic state equations of nuclear reactor is given. The dependence of ARMA model parameters on the main physical characteristics of RB nuclear reactor in Vinca is presented. Preliminary identification results are presented, observed discrepancies between theory and experiment are explained and the possibilities of identification improvement are anticipated. (author)
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus
2007-01-01
of stochastic origin can be observed in experiments. The models include a new approach to the platinum phase transition, which allows for a unification of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical behavior of the macroscopic reaction kinetics is investigated and shows good agreement...
Powering stochastic reliability models by discrete event simulation
DEFF Research Database (Denmark)
Kozine, Igor; Wang, Xiaoyun
2012-01-01
it difficult to find a solution to the problem. The power of modern computers and recent developments in discrete-event simulation (DES) software enable to diminish some of the drawbacks of stochastic models. In this paper we describe the insights we have gained based on using both Markov and DES models...
Stochastic Modelling of the Diffusion Coefficient for Concrete
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficients D is strongly dependent on the w/c ratio and the temperature....
Stochastic Robust Mathematical Programming Model for Power System Optimization
Energy Technology Data Exchange (ETDEWEB)
Liu, Cong; Changhyeok, Lee; Haoyong, Chen; Mehrotra, Sanjay
2016-01-01
This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.
AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)
Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...
A stochastic cloud model for cloud and ozone retrievals from UV measurements
International Nuclear Information System (INIS)
Efremenko, Dmitry S.; Schüssler, Olena; Doicu, Adrian; Loyola, Diego
2016-01-01
The new generation of satellite instruments provides measurements in and around the Oxygen A-band on a global basis and with a relatively high spatial resolution. These data are commonly used for the determination of cloud properties. A stochastic model and radiative transfer model, previously developed by the authors, is used as the forward model component in retrievals of cloud parameters and ozone total and partial columns. The cloud retrieval algorithm combines local and global optimization routines, and yields a retrieval accuracy of about 1% and a fast computational time. Retrieved parameters are the cloud optical thickness and the cloud-top height. It was found that the use of the independent pixel approximation instead of the stochastic cloud model leads to large errors in the retrieved cloud parameters, as well as, in the retrieved ozone height resolved partial columns. The latter can be reduced by using the stochastic cloud model to compute the optimal value of the regularization parameter in the framework of Tikhonov regularization. - Highlights: • A stochastic radiative transfer model for retrieving clouds/ozone is designed. • Errors of independent pixel approximation (IPA) for O3 total column are small. • The error of IPA for ozone profile retrieval may become large. • The use of stochastic model reduces the error of ozone profile retrieval.
Stochastic Model for the Vocabulary Growth in Natural Languages
Directory of Open Access Journals (Sweden)
Martin Gerlach
2013-05-01
Full Text Available We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of words: (i a finite number of core words, which have higher frequency and do not affect the probability of a new word to be used, and (ii the remaining virtually infinite number of noncore words, which have lower frequency and, once used, reduce the probability of a new word to be used in the future. Our model relies on a careful analysis of the Google Ngram database of books published in the last centuries, and its main consequence is the generalization of Zipf’s and Heaps’ law to two-scaling regimes. We confirm that these generalizations yield the best simple description of the data among generic descriptive models and that the two free parameters depend only on the language but not on the database. From the point of view of our model, the main change on historical time scales is the composition of the specific words included in the finite list of core words, which we observe to decay exponentially in time with a rate of approximately 30 words per year for English.
A stochastic differential equation model of diurnal cortisol patterns
Brown, E. N.; Meehan, P. M.; Dempster, A. P.
2001-01-01
Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.
A Stochastic Approach to Noise Modeling for Barometric Altimeters
Directory of Open Access Journals (Sweden)
Angelo Maria Sabatini
2013-11-01
Full Text Available The question whether barometric altimeters can be applied to accurately track human motions is still debated, since their measurement performance are rather poor due to either coarse resolution or drifting behavior problems. As a step toward accurate short-time tracking of changes in height (up to few minutes, we develop a stochastic model that attempts to capture some statistical properties of the barometric altimeter noise. The barometric altimeter noise is decomposed in three components with different physical origin and properties: a deterministic time-varying mean, mainly correlated with global environment changes, and a first-order Gauss-Markov (GM random process, mainly accounting for short-term, local environment changes, the effects of which are prominent, respectively, for long-time and short-time motion tracking; an uncorrelated random process, mainly due to wideband electronic noise, including quantization noise. Autoregressive-moving average (ARMA system identification techniques are used to capture the correlation structure of the piecewise stationary GM component, and to estimate its standard deviation, together with the standard deviation of the uncorrelated component. M-point moving average filters used alone or in combination with whitening filters learnt from ARMA model parameters are further tested in few dynamic motion experiments and discussed for their capability of short-time tracking small-amplitude, low-frequency motions.
Reflected stochastic differential equation models for constrained animal movement
Hanks, Ephraim M.; Johnson, Devin S.; Hooten, Mevin B.
2017-01-01
Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.
Estimation of Stochastic Volatility Models by Nonparametric Filtering
DEFF Research Database (Denmark)
Kanaya, Shin; Kristensen, Dennis
2016-01-01
/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases...... and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties...
Wang, Xiao-Tian; Wu, Min; Zhou, Ze-Min; Jing, Wei-Shu
2012-02-01
This paper deals with the problem of discrete time option pricing using the fractional long memory stochastic volatility model with transaction costs. Through the 'anchoring and adjustment' argument in a discrete time setting, a European call option pricing formula is obtained.
Stochastic quantization of fermionic theories: renormalization of the massive Thirring model
Energy Technology Data Exchange (ETDEWEB)
Brunelli, J C
1992-10-01
Using the Langevin approach for stochastic processes we study the renormalizability of the massive Thirring model. At finite fictitious time, we prove the absence of induced quadrilinear counterterms by verifying the cancellation of the divergencies of graphs with four external lines. This implies that the vanishing of the renormalization group beta function already occurs at finite times. (author). 12 refs., 3 figs.
A stochastic aerodynamic model for stationary blades in unsteady 3D wind fields
International Nuclear Information System (INIS)
Fluck, Manuel; Crawford, Curran
2016-01-01
Dynamic loads play an important roll in the design of wind turbines, but establishing the life-time aerodynamic loads (e.g. extreme and fatigue loads) is a computationally expensive task. Conventional (deterministic) methods to analyze long term loads, which rely on the repeated analysis of multiple different wind samples, are usually too expensive to be included in optimization routines. We present a new stochastic approach, which solves the aerodynamic system equations (Lagrangian vortex model) in the stochastic space, and thus arrive directly at a stochastic description of the coupled loads along a turbine blade. This new approach removes the requirement of analyzing multiple different realizations. Instead, long term loads can be extracted from a single stochastic solution, a procedure that is obviously significantly faster. Despite the reduced analysis time, results obtained from the stochastic approach match deterministic result well for a simple test-case (a stationary blade). In future work, the stochastic method will be extended to rotating blades, thus opening up new avenues to include long term loads into turbine optimization. (paper)
Multi-scenario modelling of uncertainty in stochastic chemical systems
International Nuclear Information System (INIS)
Evans, R. David; Ricardez-Sandoval, Luis A.
2014-01-01
Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent on the uncertain input and reaction system. •The model was computationally more efficient than Kinetic Monte Carlo
International Nuclear Information System (INIS)
Laurens, J.M.
1985-01-01
A computer code was written to model food chains in order to estimate the internal and external doses, for stochastic and non-stochastic effects, on humans (adults and infants). Results are given for 67 radionuclides, for unit concentration in water (1 Bq/L) and in atmosphere (1 Bq/m 3 )
DEFF Research Database (Denmark)
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode
2009-01-01
are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE1 approximation......The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model...... development, J. Pharmacokinet. Pharmacodyn. 32 (February(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8...
The Role of Stochastic Models in Interpreting the Origins of Biological Chirality
Directory of Open Access Journals (Sweden)
Gábor Lente
2010-04-01
Full Text Available This review summarizes recent stochastic modeling efforts in the theoretical research aimed at interpreting the origins of biological chirality. Stochastic kinetic models, especially those based on the continuous time discrete state approach, have great potential in modeling absolute asymmetric reactions, experimental examples of which have been reported in the past decade. An overview of the relevant mathematical background is given and several examples are presented to show how the significant numerical problems characteristic of the use of stochastic models can be overcome by non-trivial, but elementary algebra. In these stochastic models, a particulate view of matter is used rather than the concentration-based view of traditional chemical kinetics using continuous functions to describe the properties system. This has the advantage of giving adequate description of single-molecule events, which were probably important in the origin of biological chirality. The presented models can interpret and predict the random distribution of enantiomeric excess among repetitive experiments, which is the most striking feature of absolute asymmetric reactions. It is argued that the use of the stochastic kinetic approach should be much more widespread in the relevant literature.
Stochastic lattice model of synaptic membrane protein domains.
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
DEFF Research Database (Denmark)
Pang, Kar Mun; Jangi, Mehdi; Bai, Xue-Song
2018-01-01
This paper aims to simulate diesel spray flames across a wide range of engine-like conditions using the Eulerian Stochastic Field probability density function (ESF-PDF) model. The ESF model is coupled with the Chemistry Coordinate Mapping approach to expedite the calculation. A convergence study...... is carried out for a number of stochastic fields at five different conditions, covering both conventional diesel combustion and low-temperature combustion regimes. Ignition delay time, flame lift-off length as well as distributions of temperature and various combustion products are used to evaluate...... the performance of the model. The peak values of these properties generated using thirty-two stochastic fields are found to converge, with a maximum relative difference of 27% as compared to those from a greater number of stochastic fields. The ESF-PDF model with thirty-two stochastic fields performs reasonably...
Stochastic Modeling of Radioactive Material Releases
Energy Technology Data Exchange (ETDEWEB)
Andrus, Jason [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pope, Chad [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
Stochastic Modeling of Radioactive Material Releases
International Nuclear Information System (INIS)
Andrus, Jason; Pope, Chad
2015-01-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
Streeter, Lee
2017-07-01
Time-of-flight range imaging is analyzed using stochastic calculus. Through a series of interpretations and simplifications, the stochastic model leads to two methods for estimating linear radial velocity: maximum likelihood estimation on the transition probability distribution between measurements, and a new method based on analyzing the measured correlation waveform and its first derivative. The methods are tested in a simulated motion experiment from (-40)-(+40) m/s, with data from a camera imaging an object on a translation stage. In tests maximum likelihood is slow and unreliable, but when it works it estimates the linear velocity with standard deviation of 1 m/s or better. In comparison the new method is fast and reliable but works in a reduced velocity range of (-20)-(+20) m/s with standard deviation ranging from 3.5 m/s to 10 m/s.
Risk-sensitive control of stochastic hybrid systems on infinite time horizon
Directory of Open Access Journals (Sweden)
Runolfsson Thordur
1999-01-01
Full Text Available A risk-sensitive optimal control problem is considered for a hybrid system that consists of continuous time diffusion process that depends on a discrete valued mode variable that is modeled as a Markov chain. Optimality conditions are presented and conditions for the existence of optimal controls are derived. It is shown that the optimal risk-sensitive control problem is equivalent to the upper value of an associated stochastic differential game, and insight into the contributions of the noise input and mode variable to the risk sensitivity of the cost functional is given. Furthermore, it is shown that due to the mode variable risk sensitivity, the equivalence relationship that has been observed between risk-sensitive and H ∞ control in the nonhybrid case does not hold for stochastic hybrid systems.
Contribution to the stochastically studies of space-time dependable hydrological processes
International Nuclear Information System (INIS)
Kjaevski, Ivancho
2002-12-01
One of the fundaments of today's planning and water economy is Science of Hydrology. Science of Hydrology through the history had followed the development of the water management systems. Water management systems, during the time from single-approach evolved to complex and multi purpose systems. The dynamic and development of the today's society contributed for increasing the demand of clean water, and in the same time, the resources of clean water in the nature are reduced. In this kind of conditions, water management systems should resolve problems that are more complicated during managing of water sources. Solving the problems in water management, enable development and applying new methods and technologies in planning and management with water resources and water management systems like: systematical analyses, operational research, hierarchy decisions, expert systems, computer technology etc. Planning and management of water sources needs historical measured data for hydro metrological processes. In our country there are data of hydro metrological processes in period of 50-70, but in some Europe countries there are data more than 100 years. Water economy trends follow the hydro metrological trend research. The basic statistic techniques like sampling, probability distribution function, correlation and regression, are used about one intended and simple water management problems. Solving new problems about water management needs using of space-time stochastic technique, modem mathematical and statistical techniques during simulation and optimization of complex water systems. We need tree phases of development of the techniques to get secure hydrological models: i) Estimate the quality of hydro meteorological data, analyzing of their consistency, and homogeneous; ii) Structural analyze of hydro meteorological processes; iii) Mathematical models for modeling hydro meteorological processes. Very often, the third phase is applied for analyzing and modeling of hydro
Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism
Directory of Open Access Journals (Sweden)
Jian Zhang
2017-01-01
Full Text Available A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.
Stochastic Modelling of Wireless Energy Transfer
Veilleux, Shaun; Almaghasilah, Ahmed; Abedi, Ali; Wilkerson, DeLisa
2017-01-01
This study investigates the efficiency of a new method of powering remote sensors by the means of wireless energy transfer. The increased use of sensors for data collection comes with the inherent cost of supplying power from sources such as power cables or batteries. Wireless energy transfer technology eliminates the need for power cables or periodic battery replacement. The time and cost of setting up or expanding a sensor network will be reduced while allowing sensors to be placed in areas where running power cables or battery replacement is not feasible. This paper models wireless channels for power and data separately. Smart scheduling for the data channel is proposed to avoid transmitting data on a noisy channel where the probability of data loss is high to improve power efficiency. Analytical models have been developed and verified using simulations.
Response spectrum analysis of a stochastic seismic model
International Nuclear Information System (INIS)
Kimura, Koji; Sakata, Masaru; Takemoto, Shinichiro.
1990-01-01
The stochastic response spectrum approach is presented for predicting the dynamic behavior of structures to earthquake excitation expressed by a random process, one of whose sample functions can be regarded as a recorded strong-motion earthquake accelerogram. The approach consists of modeling recorded ground motion by a random process and the root-mean-square response (rms) analysis of a single-degree-of-freedom system by using the moment equations method. The stochastic response spectrum is obtained as a plot of the maximum rms response versus the natural period of the system and is compared with the conventional response spectrum. (author)
Stochastic geometry, spatial statistics and random fields models and algorithms
2015-01-01
Providing a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, this volume places a special emphasis on fundamental classes of models and algorithms as well as on their applications, for example in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R, which are widely used in the mathematical community. It can be regarded as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered, with a focus on asymptotic methods.
International Nuclear Information System (INIS)
Bieda, Bogusław
2013-01-01
The paper is concerned with application and benefits of MC simulation proposed for estimating the life of a modern municipal solid waste (MSW) landfill. The software Crystal Ball® (CB), simulation program that helps analyze the uncertainties associated with Microsoft® Excel models by MC simulation, was proposed to calculate the transit time contaminants in porous media. The transport of contaminants in soil is represented by the one-dimensional (1D) form of the advection–dispersion equation (ADE). The computer program CONTRANS written in MATLAB language is foundation to simulate and estimate the thickness of landfill compacted clay liner. In order to simplify the task of determining the uncertainty of parameters by the MC simulation, the parameters corresponding to the expression Z2 taken from this program were used for the study. The tested parameters are: hydraulic gradient (HG), hydraulic conductivity (HC), porosity (POROS), linear thickness (TH) and diffusion coefficient (EDC). The principal output report provided by CB and presented in the study consists of the frequency chart, percentiles summary and statistics summary. Additional CB options provide a sensitivity analysis with tornado diagrams. The data that was used include available published figures as well as data concerning the Mittal Steel Poland (MSP) S.A. in Kraków, Poland. This paper discusses the results and show that the presented approach is applicable for any MSW landfill compacted clay liner thickness design. -- Highlights: ► Numerical simulation of waste in porous media is proposed. ► Statistic outputs based on correct assumptions about probability distribution are presented. ► The benefits of a MC simulation are examined. ► The uniform probability distribution is studied. ► I report a useful tool applied to determine the life of a modern MSW landfill.
Energy Technology Data Exchange (ETDEWEB)
Bieda, Boguslaw, E-mail: bbieda@zarz.agh.edu.pl
2013-01-01
The paper is concerned with application and benefits of MC simulation proposed for estimating the life of a modern municipal solid waste (MSW) landfill. The software Crystal Ball Registered-Sign (CB), simulation program that helps analyze the uncertainties associated with Microsoft Registered-Sign Excel models by MC simulation, was proposed to calculate the transit time contaminants in porous media. The transport of contaminants in soil is represented by the one-dimensional (1D) form of the advection-dispersion equation (ADE). The computer program CONTRANS written in MATLAB language is foundation to simulate and estimate the thickness of landfill compacted clay liner. In order to simplify the task of determining the uncertainty of parameters by the MC simulation, the parameters corresponding to the expression Z2 taken from this program were used for the study. The tested parameters are: hydraulic gradient (HG), hydraulic conductivity (HC), porosity (POROS), linear thickness (TH) and diffusion coefficient (EDC). The principal output report provided by CB and presented in the study consists of the frequency chart, percentiles summary and statistics summary. Additional CB options provide a sensitivity analysis with tornado diagrams. The data that was used include available published figures as well as data concerning the Mittal Steel Poland (MSP) S.A. in Krakow, Poland. This paper discusses the results and show that the presented approach is applicable for any MSW landfill compacted clay liner thickness design. -- Highlights: Black-Right-Pointing-Pointer Numerical simulation of waste in porous media is proposed. Black-Right-Pointing-Pointer Statistic outputs based on correct assumptions about probability distribution are presented. Black-Right-Pointing-Pointer The benefits of a MC simulation are examined. Black-Right-Pointing-Pointer The uniform probability distribution is studied. Black-Right-Pointing-Pointer I report a useful tool applied to determine the life of a
Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.
Kang, Yun; Lanchier, Nicolas
2011-06-01
We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the
Directory of Open Access Journals (Sweden)
Giorgos Minas
2017-07-01
Full Text Available In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA overcomes the main limitations of the standard Linear Noise Approximation (LNA to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.
Stochastic Modelling as a Tool for Seismic Signals Segmentation
Directory of Open Access Journals (Sweden)
Daniel Kucharczyk
2016-01-01
Full Text Available In order to model nonstationary real-world processes one can find appropriate theoretical model with properties following the analyzed data. However in this case many trajectories of the analyzed process are required. Alternatively, one can extract parts of the signal that have homogenous structure via segmentation. The proper segmentation can lead to extraction of important features of analyzed phenomena that cannot be described without the segmentation. There is no one universal method that can be applied for all of the phenomena; thus novel methods should be invented for specific cases. They might address specific character of the signal in different domains (time, frequency, time-frequency, etc.. In this paper we propose two novel segmentation methods that take under consideration the stochastic properties of the analyzed signals in time domain. Our research is motivated by the analysis of vibration signals acquired in an underground mine. In such signals we observe seismic events which appear after the mining activity, like blasting, provoked relaxation of rock, and some unexpected events, like natural rock burst. The proposed segmentation procedures allow for extraction of such parts of the analyzed signals which are related to mentioned events.
Elliott, Thomas J.; Gu, Mile
2018-03-01
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine.
The threshold of a stochastic SIQS epidemic model
Zhang, Xiao-Bing; Huo, Hai-Feng; Xiang, Hong; Shi, Qihong; Li, Dungang
2017-09-01
In this paper, we present the threshold of a stochastic SIQS epidemic model which determines the extinction and persistence of the disease. Furthermore, we find that noise can suppress the disease outbreak. Numerical simulations are also carried out to confirm the analytical results.
Stochasticity thresholds in the Fermi-Pasta-Ulam model
International Nuclear Information System (INIS)
Callegari, B.; Galgani, L.; Milan Univ.
1979-01-01
The authors consider the celebrated model of Fermi, Pasta and Ulam and give a numerical estimate for its thresholds of stochasticity, thus determining a critical energy as a function of the frequency of the corresponding oscillators. The results turn out to be qualitatively similar to those already obtained for a chain of particles with nearest-neighbour Lennard-Jones interaction potential. (author)
A stochastic large deformation model for computational anatomy
DEFF Research Database (Denmark)
Arnaudon, Alexis; Holm, Darryl D.; Pai, Akshay Sadananda Uppinakudru
2017-01-01
In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation...
Stochasticity thresholds in the Fermi-Pasta-Ulam model
Energy Technology Data Exchange (ETDEWEB)
Callegari, B [Ferrara Univ. (Italy). Ist. di Matematica; Carotta, M C; Ferrario, C [Ferrara Univ. (Italy). Ist. di Fisica; Lo Vecchio, G [Ferrara Univ. (Italy). Ist. di Fisica; Gruppo Nazionale di Struttura della Materia, Ferrara (Italy)); Galgani, L [Milan Univ. (Italy). Ist. di Fisica; Milan Univ. (Italy). Ist. di Matematica)
1979-12-11
The authors consider the celebrated model of Fermi, Pasta and Ulam and give a numerical estimate for its thresholds of stochasticity, thus determining a critical energy as a function of the frequency of the corresponding oscillators. The results turn out to be qualitatively similar to those already obtained for a chain of particles with nearest-neighbour Lennard-Jones interaction potential.
Stochastic Online Learning in Dynamic Networks under Unknown Models
2016-08-02
The key is to develop online learning strategies at each individual node. Specifically, through local information exchange with its neighbors, each...infinitely repeated game with incomplete information and developed a dynamic pricing strategy referred to as Competitive and Cooperative Demand Learning...Stochastic Online Learning in Dynamic Networks under Unknown Models This research aims to develop fundamental theories and practical algorithms for
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
Model tracking dual stochastic controller design under irregular internal noises
International Nuclear Information System (INIS)
Lee, Jong Bok; Heo, Hoon; Cho, Yun Hyun; Ji, Tae Young
2006-01-01
Although many methods about the control of irregular external noise have been introduced and implemented, it is still necessary to design a controller that will be more effective and efficient methods to exclude for various noises. Accumulation of errors due to model tracking, internal noises (thermal noise, shot noise and l/f noise) that come from elements such as resistor, diode and transistor etc. in the circuit system and numerical errors due to digital process often destabilize the system and reduce the system performance. New stochastic controller is adopted to remove those noises using conventional controller simultaneously. Design method of a model tracking dual controller is proposed to improve the stability of system while removing external and internal noises. In the study, design process of the model tracking dual stochastic controller is introduced that improves system performance and guarantees robustness under irregular internal noises which can be created internally. The model tracking dual stochastic controller utilizing F-P-K stochastic control technique developed earlier is implemented to reveal its performance via simulation
Hydrological modeling using a multi-site stochastic weather generator
Weather data is usually required at several locations over a large watershed, especially when using distributed models for hydrological simulations. In many applications, spatially correlated weather data can be provided by a multi-site stochastic weather generator which considers the spatial correl...
Optimal Tax Reduction by Depreciation : A Stochastic Model
Berg, M.; De Waegenaere, A.M.B.; Wielhouwer, J.L.
1996-01-01
This paper focuses on the choice of a depreciation method, when trying to minimize the expected value of the present value of future tax payments.In a quite general model that allows for stochastic future cash- ows and a tax structure with tax brackets, we determine the optimal choice between the
Stochastic models in risk theory and management accounting
Brekelmans, R.C.M.
2000-01-01
This thesis deals with stochastic models in two fields: risk theory and management accounting. Firstly, two extensions of the classical risk process are analyzed. A method is developed that computes bounds of the probability of ruin for the classical risk rocess extended with a constant interest
Analyzing Properties of Stochastic Business Processes By Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2013-01-01
This chapter presents an approach to precise formal analysis of business processes with stochastic properties. The method presented here allows for both qualitative and quantitative properties to be individually analyzed at design time without requiring a full specification. This provides...... an effective means to explore possible designs for a business process and to debug any flaws....
Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters
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Wen Xu
2016-10-01
Full Text Available Time-varying volatility is common in macroeconomic data and has been incorporated into macroeconomic models in recent work. Dynamic panel data models have become increasingly popular in macroeconomics to study common relationships across countries or regions. This paper estimates dynamic panel data models with stochastic volatility by maximizing an approximate likelihood obtained via Rao-Blackwellized particle filters. Monte Carlo studies reveal the good and stable performance of our particle filter-based estimator. When the volatility of volatility is high, or when regressors are absent but stochastic volatility exists, our approach can be better than the maximum likelihood estimator which neglects stochastic volatility and generalized method of moments (GMM estimators.
The threshold of a stochastic delayed SIR epidemic model with vaccination
Liu, Qun; Jiang, Daqing
2016-11-01
In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number Rbar0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.
A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis
Pham, Minh Tu; Vernieuwe, Hilde; De Baets, Bernard; Verhoest, Niko E. C.
2018-02-01
A hydrological impact analysis concerns the study of the consequences of certain scenarios on one or more variables or fluxes in the hydrological cycle. In such an exercise, discharge is often considered, as floods originating from extremely high discharges often cause damage. Investigating the impact of extreme discharges generally requires long time series of precipitation and evapotranspiration to be used to force a rainfall-runoff model. However, such kinds of data may not be available and one should resort to stochastically generated time series, even though the impact of using such data on the overall discharge, and especially on the extreme discharge events, is not well studied. In this paper, stochastically generated rainfall and corresponding evapotranspiration time series, generated by means of vine copulas, are used to force a simple conceptual hydrological model. The results obtained are comparable to the modelled discharge using observed forcing data. Yet, uncertainties in the modelled discharge increase with an increasing number of stochastically generated time series used. Notwithstanding this finding, it can be concluded that using a coupled stochastic rainfall-evapotranspiration model has great potential for hydrological impact analysis.
Stochastic population oscillations in spatial predator-prey models
International Nuclear Information System (INIS)
Taeuber, Uwe C
2011-01-01
It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase.
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Stochastic and simulation models of maritime intercept operations capabilities
Sato, Hiroyuki
2005-01-01
The research formulates and exercises stochastic and simulation models to assess the Maritime Intercept Operations (MIO) capabilities. The models focus on the surveillance operations of the Maritime Patrol Aircraft (MPA). The analysis using the models estimates the probability with which a terrorist vessel (Red) is detected, correctly classified, and escorted for intensive investigation and neutralization before it leaves an area of interest (AOI). The difficulty of obtaining adequate int...
Extinction threshold of a population in spatial and stochastic model
Soroka, Yevheniia; Rublyov, Bogdan
2016-01-01
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically, we studied how the critical values for the model parameters that separate the cases of extinction and persistence depend on the spatial scales of the competition and dispersal kernels. We compared the simulations and analytical results to examine if and how ...
Directory of Open Access Journals (Sweden)
Shichao Sun
2015-01-01
Full Text Available This paper addressed the vehicle routing problem (VRP in large-scale urban transportation networks with stochastic time-dependent (STD travel times. The subproblem which is how to find the optimal path connecting any pair of customer nodes in a STD network was solved through a robust approach without requiring the probability distributions of link travel times. Based on that, the proposed STD-VRP model can be converted into solving a normal time-dependent VRP (TD-VRP, and algorithms for such TD-VRPs can also be introduced to obtain the solution. Numerical experiments were conducted to address STD-VRPTW of practical sizes on a real world urban network, demonstrated here on the road network of Shenzhen, China. The stochastic time-dependent link travel times of the network were calibrated by historical floating car data. A route construction algorithm was applied to solve the STD problem in 4 delivery scenarios efficiently. The computational results showed that the proposed STD-VRPTW model can improve the level of customer service by satisfying the time-window constraint under any circumstances. The improvement can be very significant especially for large-scale network delivery tasks with no more increase in cost and environmental impacts.
Dependence of the number of dealers in a stochastic dealer model
Yamada, Kenta; Takayasu, Hideki; Takayasu, Misako
2010-04-01
We numerically analyze an artificial market model consisted of N dealers with time dependent stochastic strategy. Observing the change of market price statistics for different values of N, it is shown that the statistical properties are almost same when the dealer number is larger than about 30.
The Risk-Return Tradeoff and Leverage Effect in a Stochastic Volatility-in-Mean Model
DEFF Research Database (Denmark)
Christensen, Bent Jesper; Posedel, Petra
We study the risk premium and leverage effect in the S&P500 market using the stochastic volatility-in-mean model of Barndor¤-Nielsen & Shephard (2001). The Merton (1973, 1980) equilibrium asset pricing condition linking the conditional mean and conditional variance of discrete time returns is rei...