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...
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
Granita, Bahar, Arifah
2015-10-01
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.
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,...
Parzen, Emanuel
2015-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
Stochastic Processes via the Pathway Model
Directory of Open Access Journals (Sweden)
Arak M. Mathai
2015-04-01
Full Text Available After collecting data from observations or experiments, the next step is to analyze the data to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the model. In this article, the input-output type mechanism is considered first, where reaction, diffusion, reaction-diffusion, and production-destruction type physical situations can fit in. Then techniques are described to produce thicker or thinner tails (power law behavior in stochastic models. Then the pathway idea is described where one can switch to different functional forms of the probability density function through a parameter called the pathway parameter. The paper is a continuation of related solar neutrino research published previously in this journal.
Stochastic Gompertzian model for breast cancer growth process
Mazlan, Mazma Syahidatul Ayuni Binti; Rosli, Norhayati
2017-05-01
In this paper, a stochastic Gompertzian model is developed to describe the growth process of a breast cancer by incorporating the noisy behavior into a deterministic Gompertzian model. The prediction quality of the stochastic Gompertzian model is measured by comparing the simulated result with the clinical data of breast cancer growth. The kinetic parameters of the model are estimated via maximum likelihood procedure. 4-stage stochastic Runge-Kutta (SRK4) is used to simulate the sample path of the model. Low values of mean-square error (MSE) of stochastic model indicate good fits. It is shown that the stochastic Gompertzian model is adequate in explaining the breast cancer growth process compared to the deterministic model counterpart.
Constructing stochastic models from deterministic process equations by propensity adjustment
Directory of Open Access Journals (Sweden)
Wu Jialiang
2011-11-01
Full Text Available Abstract Background Gillespie's stochastic simulation algorithm (SSA for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases. Results We propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. Conclusions The construction of a stochastic
Frank, T D
2002-07-01
Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.
Modelling Real World Using Stochastic Processes and Filtration
Directory of Open Access Journals (Sweden)
Jaeger Peter
2016-03-01
Full Text Available First we give an implementation in Mizar [2] basic important definitions of stochastic finance, i.e. filtration ([9], pp. 183 and 185, adapted stochastic process ([9], p. 185 and predictable stochastic process ([6], p. 224. Second we give some concrete formalization and verification to real world examples.
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Energy Technology Data Exchange (ETDEWEB)
Ng, B
2006-10-12
This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.
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...
Quantitative sociodynamics stochastic methods and models of social interaction processes
Helbing, Dirk
1995-01-01
Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioural changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics but they have very often proved their explanatory power in chemistry, biology, economics and the social sciences. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces the most important concepts from nonlinear dynamics (synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches a very fundamental dynamic model is obtained which seems to open new perspectives in the social sciences. It includes many established models as special cases, e.g. the log...
Quantitative Sociodynamics Stochastic Methods and Models of Social Interaction Processes
Helbing, Dirk
2010-01-01
This new edition of Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioral changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics and mathematics, but they have very often proven their explanatory power in chemistry, biology, economics and the social sciences as well. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces important concepts from nonlinear dynamics (e.g. synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches, a fundamental dynamic model is obtained, which opens new perspectives in the social sciences. It includes many established models a...
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 Fractional Order Recovery SIR Model from a Stochastic Process.
Angstmann, C N; Henry, B I; McGann, A V
2016-03-01
Over the past several decades, there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an ad hoc manner. These models may be mathematically interesting, but their relevance is uncertain. Here we develop an SIR model for an epidemic, including vital dynamics, from an underlying stochastic process. We show how fractional differential operators arise naturally in these models whenever the recovery time from the disease is power-law distributed. This can provide a model for a chronic disease process where individuals who are infected for a long time are unlikely to recover. The fractional order recovery model is shown to be consistent with the Kermack-McKendrick age-structured SIR model, and it reduces to the Hethcote-Tudor integral equation SIR model. The derivation from a stochastic process is extended to discrete time, providing a stable numerical method for solving the model equations. We have carried out simulations of the fractional order recovery model showing convergence to equilibrium states. The number of infecteds in the endemic equilibrium state increases as the fractional order of the derivative tends to zero.
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.
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.
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...... 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...... generation of pikes. When a stimulus is applied to the network, the spontaneous rings may prevail and hamper detection of the effects of the stimulus. Therefore, the spontaneous rings cannot be ignored and the response latency has to be detected on top of a background signal. Everything becomes more dicult...
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......Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can...... with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pattern formation, which has not been captured by earlier models, can be reproduced in stochastic simulations with the mesoscopic model....
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....
Verification of Stochastic Process Calculi
DEFF Research Database (Denmark)
Skrypnyuk, Nataliya
Stochastic process calculi represent widely accepted formalisms within Computer Science for modelling nondeterministic stochastic systems in a compositional way. Similar to process calculi in general, they are suited for modelling systems in a hierarchical manner, by explicitly specifying...... subsystems as well as their interdependences and communication channels. Stochastic process calculi incorporate both the quantified uncertainty on probabilities or durations of events and nondeterministic choices between several possible continuations of the system behaviour. Modelling of a system is often...
Stochastic processes - quantum physics
Energy Technology Data Exchange (ETDEWEB)
Streit, L. (Bielefeld Univ. (Germany, F.R.))
1984-01-01
The author presents an elementary introduction to stochastic processes. He starts from simple quantum mechanics and considers problems in probability, finally presenting quantum dynamics in terms of stochastic processes.
Stochastic Modelling of Shiroro River Stream flow Process
Directory of Open Access Journals (Sweden)
Musa, J. J
2013-01-01
Full Text Available 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 model involves some basic steps such as obtain stream flow record and other information, Selecting models that best describes the marginal probability distribution of flows. The flow discharge of about 22 years (1990-2011 was gotten from the Meteorological Station at Shiroro and analyzed with three different models namely; Autoregressive (AR model, Autoregressive Moving Average (ARMA model and Autoregressive Integrated Moving Average (ARIMA model. The initial model identification is done by using the autocorrelation function (ACF and partial autocorrelation function (PACF. Based on the model analysis and evaluations, proper predictions for the effective usage of the flow from the river for farming activities and generation of power for both industrial and domestic us were made. It also highlights some recommendations to be made to utilize the possible potentials of the river effectively
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
This thesis addresses stochastic modelling of turbulence with applications to wind energy in mind. The primary tool is ambit processes, a recently developed class of computationally tractable stochastic processes based on integration with respect to Lévy bases. The subject of ambit processes...... stochastic turbulence model based on ambit processes is proposed. It is shown how a prescribed isotropic covariance structure can be reproduced. Non-Gaussian turbulence models are obtained through non-Gaussian Lévy bases or through volatility modulation of Lévy bases. As opposed to spectral models operating...... is dissipated into heat due to the internal friction caused by viscosity. An existing stochastic model, also expressed in terms of ambit processes, is extended and shown to give a universal and parsimonious description of the turbulent energy dissipation. The volatility modulation, referred to above, has...
Granita, Bahar, A.
2015-03-01
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.
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.
Stochastic model of milk homogenization process using Markov's chain
A. A. Khvostov; R. S. Sumina; G. I. Kotov; Ivanov, A. V.
2016-01-01
The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model...
Energy Technology Data Exchange (ETDEWEB)
Rizzoni, G. (Michigan Univ., Ann Arbor, MI (USA). Dept. of Electrical Engineering and Computer Science)
1989-08-01
In-cylinder gas pressure has long been recognized as a fundamental measure of performance in the internal combustion engine. Among the issues that have been the subject of research in recent years is the study of the effects cyclic combustion variability has on the cycle-to-cycle and cylinder-to-cylinder fluctuations in combustion pressures. Some of the research problems pertaining to cyclic combustion variability are to reformulate from a perspective markedly different from the fluid dynamic and thermodynamic models which traditionally characterize this research: a system viewpoint is embraced to construct a stochastic model for the indicated pressure process and the dynamics of the internal combustion engine. First a deterministic model for the dynamics of the engine is described; then a stochastic model is proposed for the cylinder pressure process. The deterministic model and the stochastic representation are then tied together in a Kalman filter model. Experimental results are discussed to validate the models.
Stochastic Greybox Modeling of an Alternating Activated Sludge Process
DEFF Research Database (Denmark)
Halvgaard, Rasmus Fogtmann; Munk-Nielsen, T.; Tychsen, P.;
Summary of key findings We found a greybox model for state estimation and control of the BioDenitro process based on a reduced ASM1. We then applied Maximum Likelihood Estimation on measurements from a real full-scale waste water treatment plant to estimate the model parameters. The estimation me...
Stochastic model of milk homogenization process using Markov's chain
Directory of Open Access Journals (Sweden)
A. A. Khvostov
2016-01-01
Full Text Available The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model parameters was carried out by minimizing the standard deviation calculated from the experimental data for each fraction of dairy products fat phase. As the set of experimental data processing results of the micrographic images of fat globules of whole milk samples distribution which were subjected to homogenization at different pressures were used. Pattern Search method was used as optimization method with the Latin Hypercube search algorithm from Global Optimization Тoolbox library. The accuracy of calculations averaged over all fractions of 0.88% (the relative share of units, the maximum relative error was 3.7% with the homogenization pressure of 30 MPa, which may be due to the very abrupt change in properties from the original milk in the particle size distribution at the beginning of the homogenization process and the lack of experimental data at homogenization pressures of below the specified value. The mathematical model proposed allows to calculate the profile of volume and mass distribution of the fat phase (fat globules in the product, depending on the homogenization pressure and can be used in the laboratory and research of dairy products composition, as well as in the calculation, design and modeling of the process equipment of the dairy industry enterprises.
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...
Modeling laser velocimeter signals as triply stochastic Poisson processes
Mayo, W. T., Jr.
1976-01-01
Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.
Biologically variable respiration as a stochastic process in ventilation - a stochastic model study.
Min, Kyongyob; Hosoi, Keita; Degami, Masayuki; Kinoshita, Yoshinori
2010-01-01
Based on the fractal bronchial tree, we introduced a function of "asynchronous phasic contractions of lobular bronchiole", which would generate fluctuations in tidal volumes. Stochastic control theory was able to describe a genesis of biological variability in spontaneous respirations using a Schroedinger wave function.
Stochastic processes inference theory
Rao, Malempati M
2014-01-01
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
Stochastic simulation by image quilting of process-based geological models
DEFF Research Database (Denmark)
Hoffimann, Júlio; Scheidt, Celine; Barfod, Adrian
2017-01-01
. In this work, we further develop image quilting as a method for 3D stochastic simulation capable of mimicking the realism of process-based geological models with minimal modeling effort (i.e. parameter tuning) and at the same time condition them to a variety of data. In particular, we develop a new...
Levy-Student processes for a stochastic model of beam halos
Energy Technology Data Exchange (ETDEWEB)
Petroni, N. Cufaro [Department of Mathematics, University of Bari, and INFN Sezione di Bari, via E. Orabona 4, 70125 Bari (Italy)]. E-mail: cufaro@ba.infn.it; De Martino, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); De Siena, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); Illuminati, F. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy)
2006-06-01
We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will analyze this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) stochastic model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. In the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.
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.
Stochastic lattice gas model describing the dynamics of the SIRS epidemic process
de Souza, David R.; Tomé, Tânia
2010-03-01
We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S → I → R → S (SIRS). The open process S → I → R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations.
Tempered stable distributions stochastic models for multiscale processes
Grabchak, Michael
2015-01-01
This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.
Adiabatic reduction of a model of stochastic gene expression with jump Markov process.
Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C
2014-04-01
This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.
Modelling Meso-Scale Diffusion Processes in Stochastic Fluid Bio-Membranes
Rafii-Tabar, H
1999-01-01
The space-time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded) inclusions and horizontally placed (surface) inclusions are considered. The energetics of the membrane, as a two-dimensional (2D) meso-scale continuum sheet, is described by the Canham-Helfrich Hamiltonian, with the membrane height function treated as a stochastic process. The diffusion parameter of this process acts as the link coupling the membrane shape fluctuations to the kinematics of the inclusions. The latter is described via Ito stochastic differential equation. In addition to stochastic forces, the inclusions also experience membrane-induced deterministic forces. Our aim is to simulate the diffusion-driven aggregation of inclusions and show how the external inclusions arrive at the sites of the embedded inclusions. The model has potential use in such emerging fields as...
Goychuk, I
2001-08-01
Stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels. An exact expression for the information gain is obtained for the Poisson process with the signal-modulated spiking rate. This result allows one to generalize the conventional stochastic resonance (SR) problem (with periodic input signal) to the arbitrary signals of finite duration (nonstationary SR). Moreover, in the case of a periodic signal, the rate of information gain is compared with the conventional signal-to-noise ratio. The paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals.
Goychuk, Igor
2001-08-01
Stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels. An exact expression for the information gain is obtained for the Poisson process with the signal-modulated spiking rate. This result allows one to generalize the conventional stochastic resonance (SR) problem (with periodic input signal) to the arbitrary signals of finite duration (nonstationary SR). Moreover, in the case of a periodic signal, the rate of information gain is compared with the conventional signal-to-noise ratio. The paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals.
Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.
2013-04-01
Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.
Stochastic simulation by image quilting of process-based geological models
Hoffimann, Júlio; Scheidt, Céline; Barfod, Adrian; Caers, Jef
2017-09-01
Process-based modeling offers a way to represent realistic geological heterogeneity in subsurface models. The main limitation lies in conditioning such models to data. Multiple-point geostatistics can use these process-based models as training images and address the data conditioning problem. In this work, we further develop image quilting as a method for 3D stochastic simulation capable of mimicking the realism of process-based geological models with minimal modeling effort (i.e. parameter tuning) and at the same time condition them to a variety of data. In particular, we develop a new probabilistic data aggregation method for image quilting that bypasses traditional ad-hoc weighting of auxiliary variables. In addition, we propose a novel criterion for template design in image quilting that generalizes the entropy plot for continuous training images. The criterion is based on the new concept of voxel reuse-a stochastic and quilting-aware function of the training image. We compare our proposed method with other established simulation methods on a set of process-based training images of varying complexity, including a real-case example of stochastic simulation of the buried-valley groundwater system in Denmark.
2015-11-30
Scientific Publishing Company DOI : 10.1142/S0219024915500521 OPTION PRICING WITH A LEVY-TYPE STOCHASTIC DYNAMIC MODEL FOR STOCK PRICE PROCESS UNDER SEMI...Applebaum (2009) Levy Processes and Stochastic Calculus . Cambridge University Press. K. Back & S. R. Pliska (1991) On the fundamental theorem of asset
Modeling irregularly spaced residual series as a continuous stochastic process
Von Asmuth, J.R.; Bierkens, M.F.P.
2005-01-01
In this paper, the background and functioning of a simple but effective continuous time approach for modeling irregularly spaced residual series is presented. The basic equations were published earlier by von Asmuth et al. (2002), who used them as part of a continuous time transfer function noise mo
Essentials of stochastic processes
Durrett, Richard
2016-01-01
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...
Directory of Open Access Journals (Sweden)
Gianni Pagnini
2012-01-01
inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion, that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes, and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
Turbulence and Stochastic Processes
Celani, Antonio; Mazzino, Andrea; Pumir, Alain
sec:08-1In 1931 the monograph Analytical Methods in Probability Theory appeared, in which A.N. Kolmogorov laid the foundations for the modern theory of Markov processes [1]. According to Gnedenko: "In the history of probability theory it is difficult to find other works that changed the established points of view and basic trends in research work in such a decisive way". Ten years later, his article on fully developed turbulence provided the framework within which most, if not all, of the subsequent theoretical investigations have been conducted [2] (see e.g. the review by Biferale et al. in this volume [3]. Remarkably, the greatest advances made in the last few years towards a thorough understanding of turbulence developed from the successful marriage between the theory of stochastic processes and the phenomenology of turbulent transport of scalar fields. In this article we will summarize these recent developments which expose the direct link between the intermittency of transported fields and the statistical properties of particle trajectories advected by the turbulent flow (see also [4], and, for a more thorough review, [5]. We also discuss the perspectives of the Lagrangian approach beyond passive scalars, especially for the modeling of hydrodynamic turbulence.
Stochastic resin transfer molding process
Park, M
2016-01-01
We consider one-dimensional and two-dimensional models of stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in the two-dimensional case. We show how variability of time to fill depends on correlation lengths and smoothness of a random permeability field.
Model-free stochastic processes studied with q-wavelet-based informational tools
Energy Technology Data Exchange (ETDEWEB)
Perez, D.G. [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso (PUCV), 23-40025 Valparaiso (Chile)]. E-mail: dario.perez@ucv.cl; Zunino, L. [Centro de Investigaciones Opticas, C.C. 124 Correo Central, 1900 La Plata (Argentina) and Departamento de Ciencias Basicas, Facultad de Ingenieria, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina) and Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina)]. E-mail: lucianoz@ciop.unlp.edu.ar; Martin, M.T. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CONICET), C.C. 727, 1900 La Plata (Argentina)]. E-mail: mtmartin@venus.unlp.edu.ar; Garavaglia, M. [Centro de Investigaciones Opticas, C.C. 124 Correo Central, 1900 La Plata (Argentina) and Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina)]. E-mail: garavagliam@ciop.unlp.edu.ar; Plastino, A. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CONICET), C.C. 727, 1900 La Plata (Argentina)]. E-mail: plastino@venus.unlp.edu.ar; Rosso, O.A. [Chaos and Biology Group, Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires (Argentina)]. E-mail: oarosso@fibertel.com.ar
2007-04-30
We undertake a model-free investigation of stochastic processes employing q-wavelet based quantifiers, that constitute a generalization of their Shannon counterparts. It is shown that (i) interesting physical information becomes accessible in such a way (ii) for special q values the quantifiers are more sensitive than the Shannon ones and (iii) there exist an implicit relationship between the Hurst parameter H and q within this wavelet framework.
Mo Zhou; Joseph Buongiorno
2011-01-01
Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...
Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
Lilly, Jonathan M.; Sykulski, Adam M.; Early, Jeffrey J.; Olhede, Sofia C.
2017-08-01
Stochastic processes exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with the spectral slope at high frequencies being associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matérn process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matérn process and its relationship to fBm. An algorithm for the simulation of the Matérn process in O(NlogN) operations is given. Unlike fBm, the Matérn process is found to provide an excellent match to modeling velocities from particle trajectories in an application to two-dimensional fluid turbulence.
Ambit processes and stochastic partial differential equations
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut
Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process
Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko
2012-06-01
A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.
Mathematical model for hit phenomena as stochastic process of interactions of human interactions
Ishii, Akira; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshda, Narihiko
2011-01-01
Mathematical model for hit phenomena in entertainments in the society is presented as stochastic process of interactions of human dynamics. The model use only the time distribution of advertisement budget as input and the words of mouth (WOM) as posting in the social network system is used as the data to compare with the calculated results. The unit of time is daily. The WOM distribution in time is found to be very close to the residue distribution in time. The calculations for Japanese motion picture market due to the mathematical model agree very well with the actual residue distribution in time.
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
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
Transport properties of stochastic Lorentz models
Beijeren, H. van
1982-01-01
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 waiti
Fractional Brownian motion, the Matern process, and stochastic modeling of turbulent dispersion
Lilly, J M; Early, J J; Olhede, S C
2016-01-01
Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matern process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matern process and...
Stochastic Climate Theory and Modelling
Franzke, Christian L E; Berner, Judith; Williams, Paul D; Lucarini, Valerio
2014-01-01
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations as well as for model error representation, uncertainty quantification, data assimilation and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochast...
Stochastic processes and filtering theory
Jazwinski, Andrew H
2007-01-01
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab
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...
Models and algorithms for stochastic online scheduling
Megow, N.; Uetz, Marc Jochen; Vredeveld, T.
We consider a model for scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to traditional stochastic scheduling models, we assume that
Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science
Directory of Open Access Journals (Sweden)
Shilong Li
2017-01-01
Full Text Available Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigate the validity condition of this new model. We also discuss actuarial present values of several life annuities under this new interest model. Simulations are done to illustrate the theoretical results and the effect of parameters in interest model on actuarial present values is also analyzed.
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 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...... the stochastic cargo container load field is based on a queuing and loading policy that assumes containers are handled by a first-come-first-serve policy. The load field is assumed to be Gaussian. The ballast system is imposed to counteract the angle of heel and to regulate both the draft and the trim caused...
Energy Technology Data Exchange (ETDEWEB)
Lee, Kwang Ho; Roh, Myung Sub [KEPCO International Nuclear Graduate School, Ulsan (Korea, Republic of)
2013-10-15
There are so many different factors to consider when constructing a nuclear power plant successfully from planning to decommissioning. According to PMBOK, all projects have nine domains from a holistic project management perspective. They are equally important to all projects, however, this study focuses mostly on the processes required to manage timely completion of the project and conduct risk management. The overall objective of this study is to let you know what the risk analysis derived from scheduling of NPP project is, and understand how to implement the stochastic process modeling through risk management. Building the Nuclear Power Plant is required a great deal of time and fundamental knowledge related to all engineering. That means that integrated project scheduling management with so many activities is necessary and very important. Simulation techniques for scheduling of NPP project using Open Plan program, Crystal Ball program, and Minitab program can be useful tools for designing optimal schedule planning. Thus far, Open Plan and Monte Carlo programs have been used to calculate the critical path for scheduling network analysis. And also, Minitab program has been applied to monitor the scheduling risk. This approach to stochastic modeling through risk analysis of project activities is very useful for optimizing the schedules of activities using Critical Path Method and managing the scheduling control of NPP project. This study has shown new approach to optimal scheduling of NPP project, however, this does not consider the characteristic of activities according to the NPP site conditions. Hence, this study needs more research considering those factors.
Sulis, William H
2017-10-01
Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.
Stochastic Nature in Cellular Processes
Institute of Scientific and Technical Information of China (English)
刘波; 刘圣君; 王祺; 晏世伟; 耿轶钊; SAKATA Fumihiko; GAO Xing-Fa
2011-01-01
The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.
Stochastic dynamical model of a growing network based on self-exciting point process
Golosovsky, Michael; 10.1103/PhysRevLett.109.098701
2012-01-01
We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation history of 40,195 papers published in one year. Contrary to common belief, we found that citation dynamics of the individual papers follows the \\emph{superlinear} preferential attachment, with the exponent $\\alpha= 1.25-1.3$. Moreover, we showed that the citation process cannot be described as a memoryless Markov chain since there is substantial correlation between the present and recent citation rates of a paper. Basing on our findings we constructed a stochastic growth model of the citation network, performed numerical simulations based on this model and achieved an excellent agreement with the measured citation distributions.
ENISI SDE: A New Web-Based Tool for Modeling Stochastic Processes.
Mei, Yongguo; Carbo, Adria; Hoops, Stefan; Hontecillas, Raquel; Bassaganya-Riera, Josep
2015-01-01
Modeling and simulations approaches have been widely used in computational biology, mathematics, bioinformatics and engineering to represent complex existing knowledge and to effectively generate novel hypotheses. While deterministic modeling strategies are widely used in computational biology, stochastic modeling techniques are not as popular due to a lack of user-friendly tools. This paper presents ENISI SDE, a novel web-based modeling tool with stochastic differential equations. ENISI SDE provides user-friendly web user interfaces to facilitate adoption by immunologists and computational biologists. This work provides three major contributions: (1) discussion of SDE as a generic approach for stochastic modeling in computational biology; (2) development of ENISI SDE, a web-based user-friendly SDE modeling tool that highly resembles regular ODE-based modeling; (3) applying ENISI SDE modeling tool through a use case for studying stochastic sources of cell heterogeneity in the context of CD4+ T cell differentiation. The CD4+ T cell differential ODE model has been published [8] and can be downloaded from biomodels.net. The case study reproduces a biological phenomenon that is not captured by the previously published ODE model and shows the effectiveness of SDE as a stochastic modeling approach in biology in general and immunology in particular and the power of ENISI SDE.
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
How baryonic feedback processes can affect dark matter halos: a stochastic model
Freundlich, J.; El-Zant, A.; Combes, F.
2016-12-01
Feedback processes from stars and active galactic nuclei result in gas density fluctuations which can contribute to `heating' dark matter haloes, decrease their density at the center and hence form more realistic `cores' than the steep `cusps' predicted by cold dark matter (CDM) simulations. We present a theoretical model deriving this effect from first principles: stochastic density variations in the gas distribution perturb the gravitational potential and hence affect the halo particles. We analytically derive the velocity dispersion imparted to the CDM particles and the corresponding relaxation time, and further perform numerical simulations to show that the assumed process can indeed lead to the formation of a core in an initially cuspy halo within a timescale comparable to the derived relaxation time. This suggests that feedback-induced cusp-core transformations observed in hydrodynamic simulations of galaxy formation may be understood and parametrized in relatively simple terms.
Stochastic power flow modeling
Energy Technology Data Exchange (ETDEWEB)
1980-06-01
The stochastic nature of customer demand and equipment failure on large interconnected electric power networks has produced a keen interest in the accurate modeling and analysis of the effects of probabilistic behavior on steady state power system operation. The principle avenue of approach has been to obtain a solution to the steady state network flow equations which adhere both to Kirchhoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques. Clearly the need of the present is to develop sound techniques for producing meaningful data to serve as input. This research has addressed this end and serves to bridge the gap between electric demand modeling, equipment failure analysis, etc., and the area of algorithm development. Therefore, the scope of this work lies squarely on developing an efficient means of producing sensible input information in the form of probability distributions for the many types of solution algorithms that have been developed. Two major areas of development are described in detail: a decomposition of stochastic processes which gives hope of stationarity, ergodicity, and perhaps even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.
Stochastic Processes in Gravitropism
Directory of Open Access Journals (Sweden)
Yasmine eMeroz
2014-11-01
Full Text Available In this short review we focus on the role of noise in gravitropism of plants - the reorientation of plants according to the direction of gravity. We briefly introduce the conventional picture of static gravisensing in cells specialized in sensing. This model hinges on the sedimentation of statoliths (high in density and mass relative to other organelles to the lowest part of the sensing cell. We then present experimental observations that cannot currently be understood within this framework. Lastly we introduce some current alternative models and directions that attempt to incorporate and interpret these experimental observations, including: (i {it dynamic sensing}, where gravisensing is suggested to be enhanced by stochastic events due to thermal and mechanical noise. These events both effectively lower the threshold of response, and lead to small-distance sedimentation, allowing amplification and integration of the signal. (ii The role of the cytoskeleton in signal-to-noise modulation and (iii in signal transduction. In closing, we discuss directions that seem to either not have been explored, or that are still poorly understood.
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...
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2012-01-01
This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and
Study on impurity desorption induced by femtosecond pulse laser based on a stochastic process model
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
With the advantages on non-equilibrium heating and desorption induced by electronic transition, the femtosecond pulse laser introduces a new way for solving the problem of impurity pollution adsorbed on a solid thin film in micro-electro-mechanical systems (MEMS). A model based on stochastic processes was established for stimulated desorption induced by the femtosecond pulse laser to interpret the interaction of the optically excited hot electrons with the adsorbed molecules in a metal substrate. Numerical simulation results reveal a time-dependent desorption probability of adsorbed molecules and indicate that how key parameters of femtosecond pulse laser, such as incident laser energy flux, pulse duration, and wavelength of pulse, have a great effect on the desorption probability.
Introduction to stochastic models in biology
DEFF Research Database (Denmark)
Ditlevsen, Susanne; Samson, Adeline
2013-01-01
be exposed to influences that are not completely understood or not feasible to model explicitly. Ignoring these phenomena in the modeling may affect the analysis of the studied biological systems. Therefore there is an increasing need to extend the deterministic models to models that embrace more complex...... variations in the dynamics. A way of modeling these elements is by including stochastic influences or noise. A natural extension of a deterministic differential equations model is a system of stochastic differential equations (SDEs), where relevant parameters are modeled as suitable stochastic processes......, or stochastic processes are added to the driving system equations. This approach assumes that the dynamics are partly driven by noise....
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.
Stochastic conditional intensity processes
DEFF Research Database (Denmark)
Bauwens, Luc; Hautsch, Nikolaus
2006-01-01
model allows for a wide range of (cross-)autocorrelation structures in multivariate point processes. The model is estimated by simulated maximum likelihood (SML) using the efficient importance sampling (EIS) technique. By modeling price intensities based on NYSE trading, we provide significant evidence...
Wheeler, Tim Allan; Holder, Martin; Winner, Hermann; Kochenderfer, Mykel
2017-01-01
Accurate simulation and validation of advanced driver assistance systems requires accurate sensor models. Modeling automotive radar is complicated by effects such as multipath reflections, interference, reflective surfaces, discrete cells, and attenuation. Detailed radar simulations based on physical principles exist but are computationally intractable for realistic automotive scenes. This paper describes a methodology for the construction of stochastic automotive radar models based on deep l...
A Family of Poisson Processes for Use in Stochastic Models of Precipitation
Penland, C.
2013-12-01
Both modified Poisson processes and compound Poisson processes can be relevant to stochastic parameterization of precipitation. This presentation compares the dynamical properties of these systems and discusses the physical situations in which each might be appropriate. If the parameters describing either class of systems originate in hydrodynamics, then proper consideration of stochastic calculus is required during numerical implementation of the parameterization. It is shown here that an improper numerical treatment can have severe implications for estimating rainfall distributions, particularly in the tails of the distributions and, thus, on the frequency of extreme events.
Online Model Learning of Buildings Using Stochastic Hybrid Systems Based on Gaussian Processes
Directory of Open Access Journals (Sweden)
Hamzah Abdel-Aziz
2017-01-01
Full Text Available Dynamical models are essential for model-based control methodologies which allow smart buildings to operate autonomously in an energy and cost efficient manner. However, buildings have complex thermal dynamics which are affected externally by the environment and internally by thermal loads such as equipment and occupancy. Moreover, the physical parameters of buildings may change over time as the buildings age or due to changes in the buildings’ configuration or structure. In this paper, we introduce an online model learning methodology to identify a nonparametric dynamical model for buildings when the thermal load is latent (i.e., the thermal load cannot be measured. The proposed model is based on stochastic hybrid systems, where the discrete state describes the level of the thermal load and the continuous dynamics represented by Gaussian processes describe the thermal dynamics of the air temperature. We demonstrate the evaluation of the proposed model using two-zone and five-zone buildings. The data for both experiments are generated using the EnergyPlus software. Experimental results show that the proposed model estimates the thermal load level correctly and predicts the thermal behavior with good performance.
Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA.
Yang, Xian; Han, Rui; Guo, Yike; Bradley, Jeremy; Cox, Benita; Dickinson, Robert; Kitney, Richard
2012-01-01
Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of clinical pathway, thereby assisting
Stochastic model in microwave propagation
Energy Technology Data Exchange (ETDEWEB)
Ranfagni, A. [“Nello Carrara” Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy); Mugnai, D., E-mail: d.mugnai@ifac.cnr.it [“Nello Carrara” Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy)
2011-11-28
Further experimental results of delay time in microwave propagation are reported in the presence of a lossy medium (wood). The measurements show that the presence of a lossy medium makes the propagation slightly superluminal. The results are interpreted on the basis of a stochastic (or path integral) model, showing how this model is able to describe each kind of physical system in which multi-path trajectories are present. -- Highlights: ► We present new experimental results on electromagnetic “anomalous” propagation. ► We apply a path integral theoretical model to wave propagation. ► Stochastic processes and multi-path trajectories in propagation are considered.
Modelling predation as a capped rate stochastic process, with applications to fish recruitment
James, Alex; Paul D Baxter; Pitchford, Jonathan W
2005-01-01
Many mathematical models use functions the value of which cannot exceed some physically or biologically imposed maximum value. A model can be described as ‘capped-rate’ when the rate of change of a variable cannot exceed a maximum value. This presents no problem when the models are deterministic but, in many applications, results from deterministic models are at best misleading. The need to account for stochasticity, both demographic and environmental, in models is therefore important but, as...
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...
Erdmann, Thorsten; Schwarz, Ulrich S
2013-01-01
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of th...
The dynamics of stochastic processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...
Modelling predation as a capped rate stochastic process, with applications to fish recruitment
James, Alex; Baxter, Paul D; Pitchford, Jonathan W
2005-01-01
Many mathematical models use functions the value of which cannot exceed some physically or biologically imposed maximum value. A model can be described as ‘capped-rate’ when the rate of change of a variable cannot exceed a maximum value. This presents no problem when the models are deterministic but, in many applications, results from deterministic models are at best misleading. The need to account for stochasticity, both demographic and environmental, in models is therefore important but, as this paper shows, incorporating stochasticity into capped-rate models is not trivial. A method using queueing theory is presented, which allows randomness and spatial heterogeneity to be incorporated rigorously into capped rate models. The method is applied to the feeding and growth of fish larvae. PMID:16849207
A stochastic process model for life cycle cost analysis of nuclear power plant systems
Van der Weide, J.A.M.; Pandey, M.D.
2013-01-01
The paper presents a general stochastic model to analyze the life cycle cost of an engineering system that is affected by minor but repairable failures interrupting the operation and a major failure that would require the replacement or renewal of the failed system. It is commonly observed that the
An introduction to probability and stochastic processes
Melsa, James L
2013-01-01
Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
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...
Doubly stochastic Poisson processes in artificial neural learning.
Card, H C
1998-01-01
This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.
Applied probability and stochastic processes
Sumita, Ushio
1999-01-01
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...
Directory of Open Access Journals (Sweden)
Petras Rupšys
2015-01-01
Full Text Available A stochastic modeling approach based on the Bertalanffy law gained interest due to its ability to produce more accurate results than the deterministic approaches. We examine tree crown width dynamic with the Bertalanffy type stochastic differential equation (SDE and mixed-effects parameters. In this study, we demonstrate how this simple model can be used to calculate predictions of crown width. We propose a parameter estimation method and computational guidelines. The primary goal of the study was to estimate the parameters by considering discrete sampling of the diameter at breast height and crown width and by using maximum likelihood procedure. Performance statistics for the crown width equation include statistical indexes and analysis of residuals. We use data provided by the Lithuanian National Forest Inventory from Scots pine trees to illustrate issues of our modeling technique. Comparison of the predicted crown width values of mixed-effects parameters model with those obtained using fixed-effects parameters model demonstrates the predictive power of the stochastic differential equations model with mixed-effects parameters. All results were implemented in a symbolic algebra system MAPLE.
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.
Erdmann, Thorsten; Albert, Philipp J; Schwarz, Ulrich S
2013-11-07
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.
Erdmann, Thorsten; Albert, Philipp J.; Schwarz, Ulrich S.
2013-11-01
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2011-01-01
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d
Goad, Clyde C.; Chadwell, C. David
1993-01-01
GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the
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.
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.
On use of the alpha stable self-similar stochastic process to model aggregated VBR video traffic
Institute of Scientific and Technical Information of China (English)
Huang Tianyun
2006-01-01
The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Different methods to estimate stability parameter α and self-similar parameter H are compared. Processes to generate the linear fractional stable noise (LFSN) and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion (FBM) and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions.
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.
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.
Truccolo, Wilson
2017-01-01
Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a
Stochastic Processes in Epidemic Theory
Lefèvre, Claude; Picard, Philippe
1990-01-01
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina
2017-09-01
A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.
Schuh, Wolf-Dieter; Brockmann, Jan Martin; Kargoll, Boris; Loth, Ina
2014-05-01
The modeling of satellite measurements series pose a special challenge because of the huge amount of data and the strong correlations between the measurements. In connection with the large number of parameters the rigorous computation of an appropriate stochastic model is a demanding task. This contribution discusses the large variety of possible strategies to treat correlated measurements with constant sampling rate. At first view the regularly structured covariance matrices suggest fast Toeplitz algorithms. But the equidistant measurement series can be also interpreted as a finite sequence of a time discrete covariance stationary stochastic processes with infinite extension. The stochastic process can be represented and analyzed in different quantities in the time domain as well as in the frequency domain. The signal itself and its autocovariance function in the time domain be accompanied by the periodogram and the spectral distribution/spectral density function in the frequency domain. These four quantities and their relations in between can be clearly represented in form of a "Magic Square", which gives a good basis to analyze the stochastic process, study truncation effects and model the behavior by parametric and non parametric approaches. The focus of this study considers the pro and cons of possible strategies to decorrelate finite sequences of measurements and is motivated by GOCE gradiometer measurements. The measurement series are characterized by large correlations over long time spans with a periodic behavior with respect to the orbital period and a fragmentation of the time series into parts, due to satellite maneuvers and calibration phases. The decorrelation process is crucial for the gravity field estimation. Therefore efficient strategies are necessary to get as much signal as possible also from the highly correlated, fragmented measurements series. Special attentions has to take place to avoid data loss during the warmup phase of recursive
Lectures on Topics in Spatial Stochastic Processes
Capasso, Vincenzo; Ivanoff, B Gail; Dozzi, Marco; Dalang, Robert C; Mountford, Thomas S
2003-01-01
The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.
Stochastic models for uncertain flexible systems
Curtain, R.F.; Kotelenez, P.
1987-01-01
If a spectral operator is perturbed by an infinite-dimensional white noise process, it generates a stochastic evolution operator which has well defined second order properties. This type of stochastic bilinear spectral evolution equation may be used to model uncertainty of the higher modes in flexib
Stochastic processes in climate modeling: from Lorenz to the El-Niño recharge oscillator and beyond
Ghil, M.; Chekroun, M. D.; Simonnet, E.
2009-04-01
In the past few years, much of the climate community's work has gone toward building highly detailed, IPCC-class general circulation models (GCMs) capable of simulating climate change. In this context, subgrid-scale physics has increasingly been modeled using stochastic processes, but the broader consequences of this approach have not yet been sufficiently explored. Stochastic subgrid-scale parametrizations have substantial non-local effects on the low-frequency dynamics itself. Moreover, due to the random forcing present in these parametrizations, traditional dynamical systems concepts — e.g., strange attractors and deterministic bifurcations — are no longer appropriate. In this talk, we present and apply mathematical concepts and tools developed by L. Arnold and his Bremen school during the last two decades. These tools have not been widely exploited so far in climate research, although they offer powerful theoretical and numerical ways of investigating stochastic models. More specifically, we use random dynamical systems (RDS) theory to analyze the stochastic dynamics of climate models. To illustrate our approach, we consider at first simple conceptual models. The first example is the well-known 3-variable Lorenz (1963) model, to which we add multiplicative noise. We show how to obtain a full description of the resulting stochastic dynamics by computing this model's random attractor and its associated invariant measure. The second example is Timmermann and Jin's (GRL, 2002) nonlinear recharge-discharge model of the El Niño/Southern Oscillation (ENSO), a model that captures several essential features of ENSO physics. A multiplicative noise term is added to this TJ model to represent wind bursts. Numerical simulations of the modified TJ model's random attractor show that Smale horseshoes are excited by the multiplicative noise, even for a parameter regime in which a Hopf bifurcation occurs in the deterministic system; such intricate structures only arise in
Walker, Martin; Hall, Andrew; Basáñez, María-Gloria
2010-10-01
The importance of the mode of acquisition of infectious stages of directly-transmitted parasitic helminths has been acknowledged in population dynamics models; hosts may acquire eggs/larvae singly in a "trickle" type manner or in "clumps". Such models have shown that the mode of acquisition influences the distribution and dynamics of parasite loads, the stability of host-parasite systems and the rate of emergence of anthelmintic resistance, yet very few field studies have allowed these questions to be explored with empirical data. We have analysed individual worm weight data for the parasitic roundworm of humans, Ascaris lumbricoides, collected from a three-round chemo-expulsion study in Dhaka, Bangladesh, with the aim of discerning whether a trickle or a clumped infection process predominates. We found that hosts tend to harbour female worms of a similar weight, indicative of a clumped infection process, but acknowledged that unmeasured host heterogeneities (random effects) could not be completely excluded as a cause. Here, we complement our previous statistical analyses using a stochastic infection model to simulate sizes of individual A. lumbricoides infecting a population of humans. We use the intraclass correlation coefficient (ICC) as a quantitative measure of similarity among simulated worm sizes and explore the behaviour of this statistic under assumptions corresponding to trickle or clumped infections and unmeasured host heterogeneities. We confirm that both mechanisms are capable of generating aggregates of similar-sized worms, but that the particular pattern of ICCs described pre- and post-anthelmintic treatment in the data is more consistent with aggregation generated by clumped infections than by host heterogeneities alone. This provides support to the notion that worms may be acquired in clumps. We discuss our results in terms of the population biology of A. lumbricoides and highlight the significance of our modelling approach for the study of the
Accelerated simulation of stochastic particle removal processes in particle-resolved aerosol models
Curtis, J. H.; Michelotti, M. D.; Riemer, N.; Heath, M. T.; West, M.
2016-10-01
Stochastic particle-resolved methods have proven useful for simulating multi-dimensional systems such as composition-resolved aerosol size distributions. While particle-resolved methods have substantial benefits for highly detailed simulations, these techniques suffer from high computational cost, motivating efforts to improve their algorithmic efficiency. Here we formulate an algorithm for accelerating particle removal processes by aggregating particles of similar size into bins. We present the Binned Algorithm for particle removal processes and analyze its performance with application to the atmospherically relevant process of aerosol dry deposition. We show that the Binned Algorithm can dramatically improve the efficiency of particle removals, particularly for low removal rates, and that computational cost is reduced without introducing additional error. In simulations of aerosol particle removal by dry deposition in atmospherically relevant conditions, we demonstrate about 50-times increase in algorithm efficiency.
Accelerated simulation of stochastic particle removal processes in particle-resolved aerosol models
Energy Technology Data Exchange (ETDEWEB)
Curtis, J.H. [Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 S. Gregory St., Urbana, IL 61801 (United States); Michelotti, M.D. [Department of Computer Science, University of Illinois at Urbana–Champaign, 201 North Goodwin Avenue, Urbana, IL 61801 (United States); Riemer, N. [Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, 105 S. Gregory St., Urbana, IL 61801 (United States); Heath, M.T. [Department of Computer Science, University of Illinois at Urbana–Champaign, 201 North Goodwin Avenue, Urbana, IL 61801 (United States); West, M., E-mail: mwest@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, 1206 W. Green St., Urbana, IL 61801 (United States)
2016-10-01
Stochastic particle-resolved methods have proven useful for simulating multi-dimensional systems such as composition-resolved aerosol size distributions. While particle-resolved methods have substantial benefits for highly detailed simulations, these techniques suffer from high computational cost, motivating efforts to improve their algorithmic efficiency. Here we formulate an algorithm for accelerating particle removal processes by aggregating particles of similar size into bins. We present the Binned Algorithm for particle removal processes and analyze its performance with application to the atmospherically relevant process of aerosol dry deposition. We show that the Binned Algorithm can dramatically improve the efficiency of particle removals, particularly for low removal rates, and that computational cost is reduced without introducing additional error. In simulations of aerosol particle removal by dry deposition in atmospherically relevant conditions, we demonstrate about 50-times increase in algorithm efficiency.
Experimentally modeling stochastic processes with less memory by the use of a quantum processor.
Palsson, Matthew S; Gu, Mile; Ho, Joseph; Wiseman, Howard M; Pryde, Geoff J
2017-02-01
Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. However, the most interesting systems are often so complex that simulating their future behavior demands storing immense amounts of information regarding how they have behaved in the past. For increasingly complex systems, simulation becomes increasingly difficult and is ultimately constrained by resources such as computer memory. Recent theoretical work shows that quantum theory can reduce this memory requirement beyond ultimate classical limits, as measured by a process' statistical complexity, C. We experimentally demonstrate this quantum advantage in simulating stochastic processes. Our quantum implementation observes a memory requirement of Cq = 0.05 ± 0.01, far below the ultimate classical limit of C = 1. Scaling up this technique would substantially reduce the memory required in simulations of more complex systems.
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
Experimentally modeling stochastic processes with less memory by the use of a quantum processor
Palsson, Matthew S.; Gu, Mile; Ho, Joseph; Wiseman, Howard M.; Pryde, Geoff J.
2017-01-01
Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. However, the most interesting systems are often so complex that simulating their future behavior demands storing immense amounts of information regarding how they have behaved in the past. For increasingly complex systems, simulation becomes increasingly difficult and is ultimately constrained by resources such as computer memory. Recent theoretical work shows that quantum theory can reduce this memory requirement beyond ultimate classical limits, as measured by a process’ statistical complexity, C. We experimentally demonstrate this quantum advantage in simulating stochastic processes. Our quantum implementation observes a memory requirement of Cq = 0.05 ± 0.01, far below the ultimate classical limit of C = 1. Scaling up this technique would substantially reduce the memory required in simulations of more complex systems. PMID:28168218
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-01
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-28
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
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
Mixed effects in stochastic differential equation models
DEFF Research Database (Denmark)
Ditlevsen, Susanne; De Gaetano, Andrea
2005-01-01
maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes......maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes...
Mathematical statistics and stochastic processes
Bosq, Denis
2013-01-01
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob
Blumenthal, Adrian
2015-01-01
Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by stochastic differential equations driven by jump-diffusion processes. In addition, there are situations, where a stochastic model is based on stochastic differential equations with multiple scales. Such stochastic problems are called stiff and lead for classical ex...
A practical guide to stochastic simulations of reaction-diffusion processes
Erban, Radek; Chapman, Jonathan; Maini, Philip
2007-01-01
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the classical Gillespie algorithm for the stochastic modelling of chemical reactions. Then stochastic algorithms for modelling molecular diffusion are given. Finally, basic stochastic reaction-diffusion methods are presented. The connections between stochastic simul...
Stochastic Model of Microtubule Dynamics
Hryniv, Ostap; Martínez Esteban, Antonio
2017-10-01
We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (v>0) and the shrinking (v<0) regimes of the dynamics.
A software framework for process flow execution of stochastic multi-scale integrated models
Schmitz, Oliver; de Kok, Jean Luc; Karssenberg, Derek
2016-01-01
Dynamic environmental models use a state transition function, external inputs and parameters to simulate the change of real-world processes over time. Modellers specify the state transition function and the external inputs required in the process calculation of each time step in a component model, a
Kraenkel, R. A.; da Silva, D. J. Pamplona
2010-01-01
We consider the dynamics of a biological population described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the case where the spatial domain consists of alternating favorable and adverse patches whose sizes are distributed randomly. For the one-dimensional case we define a stochastic analogue of the classical critical patch size. We address the issue of persistence of a population and we show that the minimum fraction of the length of favorable segments to the total length is always smaller in the stochastic case than in a periodic arrangement. In this sense, spatial stochasticity favors viability of a population.
Stochastic Simulation of Process Calculi for Biology
Phillips, Andrew; Paulevé, Loïc; 10.4204/EPTCS.40.1
2010-01-01
Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed, many of which are expressive enough to generate unbounded numbers of molecular species and reactions. As a result of this expressiveness, such calculi cannot rely on standard reaction-based simulation methods, which require fixed numbers of species and reactions. Rather than implementing custom stochastic simulation algorithms for each process calculus, we propose to use a generic abstract machine that can be instantiated to a range of process calculi and a range of reaction-based simulation algorithms. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. In this short paper we give a brief summary of the generic abstract machine, and show how it can be instant...
Semiclassical analysis for diffusions and stochastic processes
Kolokoltsov, Vassili N
2000-01-01
The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.
A Stochastic Processes Toolkit for Risk Management
Damiano Brigo; Antonio Dalessandro; Matthias Neugebauer; Fares Triki
2008-01-01
In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. This tutorial aims to introduce a number of different stochastic processes that can help in grasping the essential features of risk factors describing different asset classes or behaviors. This paper does not aim at being exhaustive, but gives examples and a feeling for practically implementable models allowing for stylised features in the data. The reader may also use t...
Visualisation for Stochastic Process Algebras: The Graphic Truth
DEFF Research Database (Denmark)
Smith, Michael James Andrew; Gilmore, Stephen
2011-01-01
There have historically been two approaches to performance modelling. On the one hand, textual language-based formalisms such as stochastic process algebras allow compositional modelling that is portable and easy to manage. In contrast, graphical formalisms such as stochastic Petri nets and stoch...
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 introduct......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...
Analysis of the stochastic channel model by Saleh & Valenzuela via the theory of point processes
DEFF Research Database (Denmark)
Jakobsen, Morten Lomholt; Pedersen, Troels; Fleury, Bernard Henri
2012-01-01
In this paper we revisit the classical channel model by Saleh & Valenzuela via the theory of spatial point processes. By reformulating this model as a particular point process and by repeated application of Campbell’s Theorem we provide concise and elegant access to its overall structure and unde...
Simulating Streamer Inception From Hydrometeors as a Stochastic Process with a Particle-Based Model
Rutjes, C.; Dubinova, A.; Ebert, U.; Buitink, S.; Scholten, O.; Trinh, G. T. N.
2016-12-01
In thunderstorms, streamers (as a precursor for lightning) can be initiated from hydrometeors (droplets, graupel, ice needles, etc.) which enhance the thundercloud electric field to values above electric breakdown; and initial electrons may come from extensive air showers [1]. Typically, streamer inception from hydrometeors is theoretically studied with deterministic fluid simulations (i.e. drift-diffusion-reaction coupled with Poisson), see [1, 2, 3] and references therein. However, electrons will only multiply in the area above breakdown, which is of the order of a cubic millimeter for hydrometeors of sub-centimeter scale. Initial electron densities, even in extreme extensive air showers events, do not exceed 10 per cubic millimeter. Hence only individual electron avalanches - with their intrinsically random nature - are entering the breakdown area sequentially. On these scales, a deterministic fluid description is thus not valid. Ideally one would do fully 3D particle simulations, like in [4], but they are computationally too costly for a parameter study with many geometries. Therefore, we developed a new stochastic particle-based model to study the behavior of the system described above. We do not follow individual electrons but complete electron avalanches. We have calculated the probability distribution of streamer inception for various hydrometeor geometries, which potentially makes it possible - when having accurate enough meteorological data - to predict where, when and how many streamers in a thundercloud occur. Besides in geophysics, the new model is also important in the context of high voltage technology, and it gives new insight in the validity of the Meek-criterion for discharge inception. [1] Dubinova et al. 2015. Phys. Rev. Lett. 115(1), 015002.[2] Liu et al. 2012. Phys. Rev. Lett. 109(2), 025002.[3] Babich et al. 2016. J. Geophys. Res. Atmos. 121, 6393-6403.[4] Teunissen, T. & Ebert, U. 2016. Plasma Sources Sci. Technol. 25(4), 044005.
Visualisation for Stochastic Process Algebras: The Graphic Truth
DEFF Research Database (Denmark)
Smith, Michael James Andrew; Gilmore, Stephen
2011-01-01
a natural interface for labelling states in the model, which integrates with our interface for specifying and model checking properties in the Continuous Stochastic Logic (CSL). We describe recent improvements to the tool in terms of usability and exploiting the visualisation framework, and discuss some......There have historically been two approaches to performance modelling. On the one hand, textual language-based formalisms such as stochastic process algebras allow compositional modelling that is portable and easy to manage. In contrast, graphical formalisms such as stochastic Petri nets...... and stochastic activity networks provide an automaton-based view of the model, which may be easier to visualise, at the expense of portability. In this paper, we argue that we can achieve the benefits of both approaches by generating a graphical view of a stochastic process algebra model, which is synchronised...
Multiresolution stochastic simulations of reaction-diffusion processes.
Bayati, B; Chatelain, P.; Koumoutsakos, P.
2008-01-01
Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by ...
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.
Stochastic epidemic models: a survey
Britton, Tom
2009-01-01
This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic model properties (relying on a large community) are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.
Stochastic Simulation of Process Calculi for Biology
Directory of Open Access Journals (Sweden)
Andrew Phillips
2010-10-01
Full Text Available Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed, many of which are expressive enough to generate unbounded numbers of molecular species and reactions. As a result of this expressiveness, such calculi cannot rely on standard reaction-based simulation methods, which require fixed numbers of species and reactions. Rather than implementing custom stochastic simulation algorithms for each process calculus, we propose to use a generic abstract machine that can be instantiated to a range of process calculi and a range of reaction-based simulation algorithms. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. In this short paper we give a brief summary of the generic abstract machine, and show how it can be instantiated with the stochastic simulation algorithm known as Gillespie's Direct Method. We also discuss the wider implications of such an abstract machine, and outline how it can be used to simulate multiple calculi simultaneously within a common framework.
ECE6010 - Stochastic Processes, Spring 2006
Moon, Todd K.
2006-01-01
This course provides an introduction to stochastic processes in communications, signal processing, digital and computer systems, and control. Topics include continuous and discrete random processes, correlation and power spectral density, optimal filtering, Markov chains, and queuing theory. Technical Requirements: MATLAB
100 years after Smoluchowski: stochastic processes in cell biology
Holcman, D.; Schuss, Z.
2017-03-01
100 years after Smoluchowski introduced his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from a large number (tens of thousands) of single molecular trajectories or to study the diffusive motion of molecules, proteins or receptors. Stochastic modeling is a new step in large data analysis that serves extracting cell biology concepts. We review here Smoluchowski’s approach to stochastic processes and provide several applications for coarse-graining diffusion, studying polymer models for understanding nuclear organization and finally, we discuss the stochastic jump dynamics of telomeres across cell division and stochastic gene regulation.
Ahmet, Kara
2015-01-01
This paper presents a simple model of the provision of higher educational services that considers and exemplifies nonlinear, stochastic, and potentially chaotic processes. I use the methods of system dynamics to simulate these processes in the context of a particular sociologically interesting case, namely that of the Turkish higher education…
Stochasticity in cell biology: Modeling across levels
Pedraza, Juan Manuel
2009-03-01
Effective modeling of biological processes requires focusing on a particular level of description, and this requires summarizing de details of lower levels into effective variables and properly accounting for the constrains that other levels impose. In the context of stochasticity in gene expression, I will show how the details of the stochastic process can be characterized by a few effective parameters, which facilitates modeling but complicates interpretation of current experiments. I will show how the resulting noise can provide advantageous or deleterious phenotypic fluctuation and how noise control in the copy number control system of plasmids can change the selective pressures. This system illustrates the direct connection between molecular dynamics and evolutionary dynamics.
Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan
2015-08-15
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.
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.
Directory of Open Access Journals (Sweden)
Svetlana Strbac Savic
2015-01-01
Full Text Available Forecasting the operational efficiency of an existing underground mine plays an important role in strategic planning of production. Degree of Operating Leverage (DOL is used to express the operational efficiency of production. The forecasting model should be able to involve common time horizon, taking the characteristics of the input variables that directly affect the value of DOL. Changes in the magnitude of any input variable change the value of DOL. To establish the relationship describing the way of changing we applied multivariable grey modeling. Established time sequence multivariable response formula is also used to forecast the future values of operating leverage. Operational efficiency of production is often associated with diverse sources of uncertainties. Incorporation of these uncertainties into multivariable forecasting model enables mining company to survive in today’s competitive environment. Simulation of mean reversion process and geometric Brownian motion is used to describe the stochastic diffusion nature of metal price, as a key element of revenues, and production costs, respectively. By simulating a forecasting model, we imitate its action in order to measure its response to different inputs. The final result of simulation process is the expected value of DOL for every year of defined time horizon.
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...... dependent particle velocity into a position independent Gaussian velocity. Boundary conditions are obtained from Itos rule of stochastic differentiation. The model directly point at a canonical rule of reflection for the approximating random walk with finite time step. This reflection rule is different from...
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 Modelling of Energy Systems
DEFF Research Database (Denmark)
Andersen, Klaus Kaae
2001-01-01
equations are expressed in terms of stochastic differential equations. From a theoretical viewpoint the techniques for experimental design, parameter estimation and model validation are considered. From the practical viewpoint emphasis is put on how this methods can be used to construct models adequate...
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...
Condensation in stochastic mass transport models: beyond the zero-range process
Evans, M. R.; Waclaw, B.
2014-03-01
We consider an extension of the zero-range process to the case where the hop rate depends on the state of both departure and arrival sites. We recover the misanthrope and the target process as special cases for which the probability of the steady state factorizes over sites. We discuss conditions which lead to the condensation of particles and show that although two different hop rates can lead to the same steady state, they do so with sharply contrasting dynamics. The first case resembles the dynamics of the zero-range process, whereas the second case, in which the hop rate increases with the occupation number of both sites, is similar to instantaneous gelation models. This new ‘explosive’ condensation reveals surprisingly rich behaviour, in which the process of the condensate’s formation goes through a series of collisions between clusters of particles moving through the system at increasing speed. We perform a detailed numerical and analytical study of the dynamics of condensation: we find the speed of the moving clusters, their scattering amplitude, and their growth time. We finally show that the time to reach steady state decreases with the size of the system.
Stochastic-field cavitation model
Energy Technology Data Exchange (ETDEWEB)
Dumond, J., E-mail: julien.dumond@areva.com [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen (Germany); Magagnato, F. [Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstrasse 12, D-76131 Karlsruhe (Germany); Class, A. [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany)
2013-07-15
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 Subspace Modelling of Turbulence
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
2009-01-01
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...
Modelling of stochastic fat-tailed auto-correlated processes: an application to short-term rates
Yashkir, Olga; Yashkir, Yuriy
2003-01-01
Many financial products sensitive to daily rate changes dictate the importance of adequate modelling of short-term rates. Their intrinsic properties are investigated based on historical market data. A new short-term rate model with the non-Gaussian random driver and auto-correlation factors is introduced. Special calibration procedures for the model are presented.Short-term rate stochastic dynamics are investigated in several numerical experiments.
Sequential decision analysis for nonstationary stochastic processes
Schaefer, B.
1974-01-01
A formulation of the problem of making decisions concerning the state of nonstationary stochastic processes is given. An optimal decision rule, for the case in which the stochastic process is independent of the decisions made, is derived. It is shown that this rule is a generalization of the Bayesian likelihood ratio test; and an analog to Wald's sequential likelihood ratio test is given, in which the optimal thresholds may vary with time.
Energy Technology Data Exchange (ETDEWEB)
Hernandez Ramos, Hugo
2008-12-15
The electrical energy prices own very particular characteristics that make them different from the prices of any good which are immersed under the fluctuation of the laws of supply and demand. The present work proposes a revision and modification of the model for the prices of electrical energy based on stochastic processes, developed in 2002 by M.T. Barlow. Our model satisfactorily explains the dynamics of the prices, having as an example the case of the energy market of Alberta, CA. The proposed model is based on the power transformation of Yeo-Johnson in 2000, which does not have dominion restrictions. Also, it is assumed that the energy price depends on the demand, which is modeled as a process of Ornstein-Uhlenbeck. The proposed model was applied to real data, obtaining corresponding estimations of the interest parameters, as well as their validation. Also simulation results are shown to determine the empirical distribution of the estimators of maximum credibility of the parameters. [Spanish] Los precios de energia electrica poseen caracteristicas muy particulares que los hacen diferentes a los precios de cualquier bien que estan inmersos bajo la fluctuacion de las leyes de la oferta y la demanda. El presente trabajo propone una revision y modificacion del modelo para los precios de energia electrica basado en procesos estocasticos, desarrollado en 2002 por M. T. Barlow. Nuestro modelo explica satisfactoriamente la dinamica de los precios, teniendo como ejemplo el caso del mercado de energia de Alberta, Ca. El modelo propuesto esta basado en la transformacion potencia de Yeo-Johnson en 2000, la cual no tiene restricciones de dominio. Tambien, se asume que el precio de la energia depende de la demanda, la cual es modelada como un proceso de Ornstein-Uhlenbeck. El modelo propuesto se aplico a datos reales, obteniendo estimaciones correspondientes de los parametros de interes, asi como su validacion. Tambien se muestran resultados de simulacion para determinar la
Selected papers on noise and stochastic processes
Wax, Nelson
1954-01-01
Six classic papers on stochastic process, selected to meet the needs of physicists, applied mathematicians, and engineers. Contents: 1.Chandrasekhar, S.: Stochastic Problems in Physics and Astronomy. 2. Uhlenbeck, G. E. and Ornstein, L. S.: On the Theory of the Browninan Motion. 3. Ming Chen Wang and Uhlenbeck, G. E.: On the Theory of the Browninan Motion II. 4. Rice, S. O.: Mathematical Analysis of Random Noise. 5. Kac, Mark: Random Walk and the Theory of Brownian Motion. 6. Doob, J. L.: The Brownian Movement and Stochastic Equations. Unabridged republication of the Dover reprint (1954). Pre
Stochastic model updating using distance discrimination analysis
Institute of Scientific and Technical Information of China (English)
Deng Zhongmin; Bi Sifeng; Sez Atamturktur
2014-01-01
This manuscript presents a stochastic model updating method, taking both uncertainties in models and variability in testing into account. The updated finite element (FE) models obtained through the proposed technique can aid in the analysis and design of structural systems. The authors developed a stochastic model updating method integrating distance discrimination analysis (DDA) and advanced Monte Carlo (MC) technique to (1) enable more efficient MC by using a response surface model, (2) calibrate parameters with an iterative test-analysis correlation based upon DDA, and (3) utilize and compare different distance functions as correlation metrics. Using DDA, the influence of distance functions on model updating results is analyzed. The proposed sto-chastic method makes it possible to obtain a precise model updating outcome with acceptable cal-culation cost. The stochastic method is demonstrated on a helicopter case study updated using both Euclidian and Mahalanobis distance metrics. It is observed that the selected distance function influ-ences the iterative calibration process and thus, the calibration outcome, indicating that an integra-tion of different metrics might yield improved results.
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...
Research on nonlinear stochastic dynamical price model
Energy Technology Data Exchange (ETDEWEB)
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
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.
Stochastic Simulations of Cellular Biological Processes
2007-06-01
model kinetics of a system of chemical reactions is to use a stochastic 2. Stochastic Simulation Algorithm approach in terms of the Chemical Master...number of processors and running time) for interactive disk spae ad, herfor, my ceat meory simulations. Therefore, in addition to running in an...management problems for simulations involving a large inteative mode, foNScan as o run in ’n number of long runs or for large reaction networks. interactive
Stochastic processes from physics to finance
Paul, Wolfgang
2013-01-01
This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.
Integrated modeling and up-scaling of landfill processes and heterogeneity using stochastic approach
Bun, A.; Heimovaara, T.J.; Baviskar, S.M.; Van Turnhout, A.G.; Konstantaki, L.A.
2012-01-01
Municipal solid waste landfills are a very complex and heterogeneous systems. The waste in a landfill body is a heterogeneous mixture of a wide range of materials containing high levels of organic matter, high amounts of salts and a wide range of different organic and inorganic substances, such as heavy metals and organic solvents. A range of processes of different nature occur within landfills. Bio-geochemical processes in a landfill body lead to the development of landfill gases, a mixture ...
ON NONSTATIONARY STOCHASTIC MODELS FOR EARTHQUAKES.
Safak, Erdal; Boore, David M.
1986-01-01
A seismological stochastic model for earthquake ground-motion description is presented. Seismological models are based on the physical properties of the source and the medium and have significant advantages over the widely used empirical models. The model discussed here provides a convenient form for estimating structural response by using random vibration theory. A commonly used random process for ground acceleration, filtered white-noise multiplied by an envelope function, introduces some errors in response calculations for structures whose periods are longer than the faulting duration. An alternate random process, filtered shot-noise process, eliminates these errors.
Stochastic simulation of supercritical fluid extraction processes
Directory of Open Access Journals (Sweden)
Mizutani F. T.
2000-01-01
Full Text Available Process simulation involves the evaluation of output variables by the specification of input variables and process parameters. However, in a real process, input data and parameters cannot be known without uncertainty. This fact may limit the utilization of simulation results to predict plant behavior. In order to achieve a more realistic analysis, the procedure of stochastic simulation can be conducted. This technique is based on a large set of simulation runs where input variables and parameters are randomly selected according to adequate probability density functions. The objective of this work is to illustrate the application of a stochastic simulation procedure to the process of fractionation of orange essential oil, using supercritical carbon dioxide in a multistage extraction column. Analysis of the proposed example demonstrates the importance of the stochastic simulation to develop more reliable designs and operating conditions for a supercritical fluid extraction process.
DEFF Research Database (Denmark)
Finlay, Chris; Olsen, Nils; Gillet, Nicolas
We present a new ensemble of time-dependent magnetic field models constructed from satellite and observatory data spanning 1997-2013 that are compatible with prior information concerning the temporal spectrum of core field variations. These models allow sharper field changes compared to traditional....... We report spherical harmonic spectra, comparisons to observatory monthly means, and maps of the radial field at the core-mantle boundary, from the resulting ensemble of core field models. We find that inter-annual fluctuations in the external field (for example related to high solar-driven activity...
Stochastic Model Checking Continuous Time Markov Process%随机模型检测连续时间Markov过程
Institute of Scientific and Technical Information of China (English)
钮俊; 曾国荪; 吕新荣; 徐畅
2011-01-01
The trustworthiness of a dynamic system includes the correctness of function and the satisfiability of per formance mainly. This paper proposed an approach to verify the function and performance of a system under considera tion integratedly. Continuous-time Markov decision process (CTMDP) is a model that contains some aspects such as probabilistic choice;stochastic timing and nondeterminacy; and it is the model by which we verify function properties and analyze performance properties uniformly. We can verify the functional and performance specifications by computing the reachability probabilities in the product CTMDP. We proved the correctness of our approach; and obtained our veri fication results by using model checker MRMC(Markov Reward Model Checker). The theoretical results show that model checking CTMDP model is necessary and the model checking approach is feasible.%功能正确和性能可满足是复杂系统可信要求非常重要的两个方面.从定性验证和定量分析相结合的角度,对复杂并发系统进行功能验证和性能分析,统一地评估系统是否可信.连续时间Markov决策过程CTMDP(Continuous-time Markov decision process)能够统一刻画复杂系统的概率选择、随机时间及不确定性等重要特征.提出用CTMDP作为系统定性验证和定量分析模型,将复杂系统的功能验证和性能分析转化为CTMDP中的可达概率求解,并证明验证过程的正确性,最终借助模型检测器MRMC(Markov Reward Model Checker)实现模型检测.理论分析表明,提出的针对CTMDP模型的验证需求是必要的,验证思路和方法具有可行性.
Stochastic biophysical modeling of irradiated cells
Fornalski, Krzysztof Wojciech
2014-01-01
The paper presents a computational stochastic model of virtual cells irradiation, based on Quasi-Markov Chain Monte Carlo method and using biophysical input. The model is based on a stochastic tree of probabilities for each cell of the entire colony. Biophysics of the cells is described by probabilities and probability distributions provided as the input. The adaptation of nucleation and catastrophe theories, well known in physics, yields sigmoidal relationships for carcinogenic risk as a function of the irradiation. Adaptive response and bystander effect, incorporated into the model, improves its application. The results show that behavior of virtual cells can be successfully modeled, e.g. cancer transformation, creation of mutations, radioadaptation or radiotherapy. The used methodology makes the model universal and practical for simulations of general processes. Potential biophysical curves and relationships are also widely discussed in the paper. However, the presented theoretical model does not describe ...
DEFF Research Database (Denmark)
Finlay, Chris; Olsen, Nils; Gillet, Nicolas
. We report spherical harmonic spectra, comparisons to observatory monthly means, and maps of the radial field at the core-mantle boundary, from the resulting ensemble of core field models. We find that inter-annual fluctuations in the external field (for example related to high solar-driven activity...
Cox process representation and inference for stochastic reaction-diffusion processes
Schnoerr, David; Grima, Ramon; Sanguinetti, Guido
2016-05-01
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.
Stochastic discrete model of karstic networks
Jaquet, O.; Siegel, P.; Klubertanz, G.; Benabderrhamane, H.
Karst aquifers are characterised by an extreme spatial heterogeneity that strongly influences their hydraulic behaviour and the transport of pollutants. These aquifers are particularly vulnerable to contamination because of their highly permeable networks of conduits. A stochastic model is proposed for the simulation of the geometry of karstic networks at a regional scale. The model integrates the relevant physical processes governing the formation of karstic networks. The discrete simulation of karstic networks is performed with a modified lattice-gas cellular automaton for a representative description of the karstic aquifer geometry. Consequently, more reliable modelling results can be obtained for the management and the protection of karst aquifers. The stochastic model was applied jointly with groundwater modelling techniques to a regional karst aquifer in France for the purpose of resolving surface pollution issues.
Stability of stochastic switched SIRS models
Meng, Xiaoying; Liu, Xinzhi; Deng, Feiqi
2011-11-01
Stochastic stability problems of a stochastic switched SIRS model with or without distributed time delay are considered. By utilizing the Lyapunov methods, sufficient stability conditions of the disease-free equilibrium are established. Stability conditions about the subsystem of the stochastic switched SIRS systems are also obtained.
Stochastic Modeling of Soil Salinity
Suweis, S; Van der Zee, S E A T M; Daly, E; Maritan, A; Porporato, A; 10.1029/2010GL042495
2012-01-01
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 long term probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equation to a single stochastic differential equation driven by multiplicative Poisson noise. The novel analytical solutions 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 long-term soil salinization trend...
Stochastic resonance during a polymer translocation process.
Mondal, Debasish; Muthukumar, M
2016-04-14
We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Chemical kinetics, stochastic processes, and irreversible thermodynamics
Santillán, Moisés
2014-01-01
This book brings theories in nonlinear dynamics, stochastic processes, irreversible thermodynamics, physical chemistry, and biochemistry together in an introductory but formal and comprehensive manner. Coupled with examples, the theories are developed stepwise, starting with the simplest concepts and building upon them into a more general framework. Furthermore, each new mathematical derivation is immediately applied to one or more biological systems. The last chapters focus on applying mathematical and physical techniques to study systems such as: gene regulatory networks and ion channels. The target audience of this book are mainly final year undergraduate and graduate students with a solid mathematical background (physicists, mathematicians, and engineers), as well as with basic notions of biochemistry and cellular biology. This book can also be useful to students with a biological background who are interested in mathematical modeling, and have a working knowledge of calculus, differential equatio...
A Note on Boolean Stochastic Processes
Fidaleo, Francesco
2015-03-01
For the quantum stochastic processes generated by the Boolean commutation relations, we prove the following version of De Finetti Theorem: each of such Boolean processes is exchangeable if and only if it is independent and identically distributed with respect to the tail algebra.
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.
Institute of Scientific and Technical Information of China (English)
LIU Chang; SHI Haibo
2006-01-01
A hierarchical closed-loop production control scheme integrating scheduling, control and performance evaluation is discussed. Firstly, the production process is divided into two main hierarchies: the lower level is the physical operation level and the upper one is the management level. Secondly, the schedule template for the management level and the activity template for the physical operation level are constructed separately, the tasks in the schedule have the ability to make partial decisions, and the performance parameters are introduced into activity template. Thirdly, the two levels use different model representations: stochastic process algebra for the management level whose output is the control commands and stochastic Petri net for the physical operation level which is the execution of the control commands. Then, the integration of the two levels is the control commands mapping into the lower physical operations and the responses feeding back to the upper decision-making that are defined by some transition functions. Under the proposed scheme, the production process control of a flexible assembly is exemplified. It is concluded that the process control model has partial ability to make decision on-line for uncertain and dynamic environments and facilitates reasoning about the behaviors of the process control, and performance evaluation can be done online for real-time scheduling to ensure the global optimization.
Classical and spatial stochastic processes with applications to biology
Schinazi, Rinaldo B
2014-01-01
The revised and expanded edition of this textbook presents the concepts and applications of random processes with the same illuminating simplicity as its first edition, but with the notable addition of substantial modern material on biological modeling. While still treating many important problems in fields such as engineering and mathematical physics, the book also focuses on the highly relevant topics of cancerous mutations, influenza evolution, drug resistance, and immune response. The models used elegantly apply various classical stochastic models presented earlier in the text, and exercises are included throughout to reinforce essential concepts. The second edition of Classical and Spatial Stochastic Processes is suitable as a textbook for courses in stochastic processes at the advanced-undergraduate and graduate levels, or as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology. Reviews of the first edition: An appetizing textbook for a f...
Stochastic Power Grid Analysis Considering Process Variations
Ghanta, Praveen; Panda, Rajendran; Wang, Janet
2011-01-01
In this paper, we investigate the impact of interconnect and device process variations on voltage fluctuations in power grids. We consider random variations in the power grid's electrical parameters as spatial stochastic processes and propose a new and efficient method to compute the stochastic voltage response of the power grid. Our approach provides an explicit analytical representation of the stochastic voltage response using orthogonal polynomials in a Hilbert space. The approach has been implemented in a prototype software called OPERA (Orthogonal Polynomial Expansions for Response Analysis). Use of OPERA on industrial power grids demonstrated speed-ups of up to two orders of magnitude. The results also show a significant variation of about $\\pm$ 35% in the nominal voltage drops at various nodes of the power grids and demonstrate the need for variation-aware power grid analysis.
Irreversible stochastic processes on lattices
Energy Technology Data Exchange (ETDEWEB)
Nord, R.S.
1986-01-01
Models for irreversible random or cooperative filling of lattices are required to describe many processes in chemistry and physics. Since the filling is assumed to be irreversible, even the stationary, saturation state is not in equilibrium. The kinetics and statistics of these processes are described by recasting the master equations in infinite hierarchical form. Solutions can be obtained by implementing various techniques: refinements in these solution techniques are presented. Programs considered include random dimer, trimer, and tetramer filling of 2D lattices, random dimer filling of a cubic lattice, competitive filling of two or more species, and the effect of a random distribution of inactive sites on the filling. Also considered is monomer filling of a linear lattice with nearest neighbor cooperative effects and solve for the exact cluster-size distribution for cluster sizes up to the asymptotic regime. Additionally, a technique is developed to directly determine the asymptotic properties of the cluster size distribution. Finally cluster growth is considered via irreversible aggregation involving random walkers. In particular, explicit results are provided for the large-lattice-size asymptotic behavior of trapping probabilities and average walk lengths for a single walker on a lattice with multiple traps. Procedures for exact calculation of these quantities on finite lattices are also developed.
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...... velocity, and water level is presented. The stochastic model includes statistical uncertainty and dependency between the four stochastic variables. Further, a new stochastic model for annual maximum directional significant wave heights is presented. The model includes dependency between the maximum wave...... height from neighboring directional sectors. Numerical examples are presented where the models are calibrated using the Maximum Likelihood method to data from the central part of the North Sea. The calibration of the directional distributions is made such that the stochastic model for the omnidirectional...
A stochastic evolutionary model for survival dynamics
Fenner, Trevor; Loizou, George
2014-01-01
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. In our model, the only implicit assumption made is that the longer an actor has been in the system, the more likely it is to have failed. We derive a power-law distribution for the process and provide preliminary empirical evidence for the validity of the model from two well-known survival analysis data sets.
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.
Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
Williams Colin P.
1999-01-01
Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.
Soil Erosion as a stochastic process
Casper, Markus C.
2015-04-01
corrected experimentally. To overcome this disadvantage of our actual models, soil erosion models are needed that are able to use stochastic directly variables and parameter distributions. There are only some minor approaches in this direction. The most advanced is the model "STOSEM" proposed by Sidorchuk in 2005. In this model, only a small part of the soil erosion processes is described, the aggregate detachment and the aggregate transport by flowing water. The concept is highly simplified, for example, many parameters are temporally invariant. Nevertheless, the main problem is that our existing measurements and experiments are not geared to provide stochastic parameters (e.g. as probability density functions); in the best case they deliver a statistical validation of the mean values. Again, we get effective parameters, spatially and temporally averaged. There is an urgent need for laboratory and field experiments on overland flow structure, raindrop effects and erosion rate, which deliver information on spatial and temporal structure of soil and surface properties and processes.
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...... 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...
Russo, Tommaso; Baldi, Paolo; Parisi, Antonio; Magnifico, Giuseppe; Mariani, Stefano; Cataudella, Stefano
2009-06-21
The study of animal growth is a longstanding crucial topic of theoretical biology. In this paper we introduce a new class of stochastic growth models that enjoy two crucial properties: the growth path of an individual is monotonically increasing and the mean length at time t follows the classic von Bertalanffy model. Besides the theoretical development, the models are also tested against a large set of length-at-age data collected on Atlantic herring (Clupea harengus): the mean lengths and variances of the cohorts were directly estimated by least squares. The results show that the use of subordinators can lead to models enjoying interesting properties, in particular able to catch some specific features often observed in fish growth data. The use of subordinators seems to allow for an increased fidelity in the description of fish growth, whilst still conforming to the general parameters of the traditional von Bertalanffy equation.
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.
Stochastic transport processes in discrete biological systems
Frehland, Eckart
1982-01-01
These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz. These notes contain the results of re cent studies on the stochastic description of ion transport through biological membranes. In particular, they serve as an introduction to an unified theory of fluctuations in complex biological transport systems. We emphasize that the subject of this volume is not to introduce the mathematics of stochastic processes but to present a field of theoretical biophysics in which stochastic methods are important. In the last years the study of membrane noise has become an important method in biophysics. Valuable information on the ion transport mechanisms in membranes can be obtained from noise analysis. A number of different processes such as the opening and closing of ion channels have been shown to be sources of the measured current or voltage fluctuations. Bio logical 'transport systems can be complex. For example, the tr...
Stochastic processes and long range dependence
Samorodnitsky, Gennady
2016-01-01
This monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory). The text is organized around the probabilistic properties of stationary processes that are important for determining the presence or absence of long memory. The first few chapters serve as an overview of the general theory of stochastic processes which gives the reader sufficient background, language, and models for the subsequent discussion of long memory. The later chapters devoted to long memory begin with an introduction to the subject along with a brief history of its development, followed by a presentation of what is currently the best known approach, applicable to stationary processes with a finite second moment. The book concludes with a chapter devoted to the author’s own, less standard, point of view of long memory as a phase transition, and even includes some novel results. Most of the material in the book has not previously been publis...
Stochastic processes and applications diffusion processes, the Fokker-Planck and Langevin equations
Pavliotis, Grigorios A
2014-01-01
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to eq...
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...
Development of A Stochastic Bedload Transport Model
Tsai, C. W.; Kuai, Z.
2009-12-01
Sediment particle transport can be viewed as a Markov chain process. In a non-equilibrium condition, the interchange of sediment particles occurs not only between the bedload layer and the bed surface, but also across the interface between bedload and suspended load. We can quantify the number of saltating particles by modeling the occupancy probabilities vector of particles staying in three states, namely, the bed surface, bedload layer, and suspended sediment layer. Most bedload transport models in the literature are formulated in terms of the mean bed shear stress or flow velocity. The proposed Markovian bedload model and the bedload transport rates are governed by various transition probabilities. These transition probabilities are all functions of the bed shear stress. The stochastic property of the bed shear stress can be incorporated into the above bedload transport model knowing the probability density function of the bed shear stress. This study presents a theoretical method to compute stochastic bedload transport rates considering the stochastic fluctuation of the bed shear stress.
Multiscale Stochastic Simulation and Modeling
Energy Technology Data Exchange (ETDEWEB)
James Glimm; Xiaolin Li
2006-01-10
Acceleration driven instabilities of fluid mixing layers include the classical cases of Rayleigh-Taylor instability, driven by a steady acceleration and Richtmyer-Meshkov instability, driven by an impulsive acceleration. Our program starts with high resolution methods of numerical simulation of two (or more) distinct fluids, continues with analytic analysis of these solutions, and the derivation of averaged equations. A striking achievement has been the systematic agreement we obtained between simulation and experiment by using a high resolution numerical method and improved physical modeling, with surface tension. Our study is accompanies by analysis using stochastic modeling and averaged equations for the multiphase problem. We have quantified the error and uncertainty using statistical modeling methods.
Stochastic Flocculation Model for Cohesive Sediment Suspended in Water
National Research Council Canada - National Science Library
Hyun Jung Shin; Minwoo Son; Guan-hong Lee
2015-01-01
.... A new stochastic approach to model the flocculation process is theoretically developed and incorporated into a deterministic FGM in this study in order to calculate a size distribution of flocs...
Multiresolution stochastic simulations of reaction-diffusion processes.
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2008-10-21
Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by many-particle systems. The proposed method quantifies and efficiently handles the associated stiffness in simulating the system dynamics and its computational efficiency and accuracy are demonstrated in simulations of a model problem described by the Fisher-Kolmogorov equation. The method is general and can be applied to other many-particle models of physical processes.
Stochastic Modeling of Reinforced Concrete Structures Exposed to Chloride Attack
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Frier, Christian
2003-01-01
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 reinforcement exceeds a critical threshold value. In the present paper a stochastic model is described by which the chloride content in a reinforced concrete structure can be estimated. The chloride ingress is modeled by a 2-dimensional diffusion process and the diffusion coefficient, surface chloride...
Efficient numerical integrators for stochastic models
De Fabritiis, G; Español, P; Coveney, P V
2006-01-01
The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
Zheng, Ying; Wong, David Shan-Hill; Wang, Yan-Wei; Fang, Huajing
2014-07-01
In many batch-based industrial manufacturing processes, feedback run-to-run control is used to improve production quality. However, measurements may be expensive and cannot always be performed online. Thus, the measurement delay always exists. The metrology delay will affect the stability and performance of the process. Moreover, since quality measurements are performed offline, delay is not fixed but is stochastic in nature. In this paper, a modeling approach Takagi-Sugeno (T-S) model is presented to handle stochastic metrology delay in both single-product and mixed-product processes. Based on the Markov characteristics of the delay, the membership of the T-S model is derived. Performance indices such as the mean and the variance of the closed-loop output of the exponentially weighted moving average (EWMA) control algorithm can be derived. A steady-state error of the process output always exists, which leads the output deviating from the target. To remove the steady-state error, an algorithm called compensatory EWMA run-to-run (COM-EWMA-RtR) algorithm is proposed. The validity of the T-S model analysis and the efficiency of the proposed COM-EWMA-RtR algorithm are confirmed by simulation.
From Complex to Simple: Interdisciplinary Stochastic Models
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…
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique ap...
A Stochastic Cobweb Dynamical Model
Directory of Open Access Journals (Sweden)
Serena Brianzoni
2008-01-01
_,__0__1, and the forward predictor with probability (1−, so that the expected price at time is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.
Stochastic dynamic model of SARS spreading
Institute of Scientific and Technical Information of China (English)
SHI Yaolin
2003-01-01
Based upon the simulation of the stochastic process of infection, onset and spreading of each SARS patient, a system dynamic model of SRAS spreading is constructed. Data from Vietnam is taken as an example for Monte Carlo test. The preliminary results indicate that the time-dependent infection rate is the most important control factor for SARS spreading. The model can be applied to prediction of the course with fluctuations of the epidemics, if the previous history of the epidemics and the future infection rate under control measures are known.
Stochastic analysis in production process and ecology under uncertainty
Bieda, Bogusław
2014-01-01
The monograph addresses a problem of stochastic analysis based on the uncertainty assessment by simulation and application of this method in ecology and steel industry under uncertainty. The first chapter defines the Monte Carlo (MC) method and random variables in stochastic models. Chapter two deals with the contamination transport in porous media. Stochastic approach for Municipal Solid Waste transit time contaminants modeling using MC simulation has been worked out. The third chapter describes the risk analysis of the waste to energy facility proposal for Konin city, including the financial aspects. Environmental impact assessment of the ArcelorMittal Steel Power Plant, in Kraków - in the chapter four - is given. Thus, four scenarios of the energy mix production processes were studied. Chapter five contains examples of using ecological Life Cycle Assessment (LCA) - a relatively new method of environmental impact assessment - which help in preparing pro-ecological strategy, and which can lead to reducing t...
Verification and Planning for Stochastic Processes with Asynchronous Events
2005-01-01
IEEE Transactions on Automatic Control 38, no. 7: 1040–1059. Bartlett, M. S. 1966. An Introduction to Stochastic Processes with Special Reference to...Artificial Intelligence, 875–881, Madison, Wisconsin. AAAI Press. Çinlar, Erhan. 1975. Introduction to Stochastic Processes . Englewood Cliffs, New... to Stochastic Processes . Boston: Houghton Mifflin Company. Hoey, Jesse, Robert St-Aubin, Alan Hu, and Craig Boutilier. 1999. SPUDD: Stochastic
Prediction horizon effects on stochastic modelling hints for neural networks
Energy Technology Data Exchange (ETDEWEB)
Drossu, R.; Obradovic, Z. [Washington State Univ., Pullman, WA (United States)
1995-12-31
The objective of this paper is to investigate the relationship between stochastic models and neural network (NN) approaches to time series modelling. Experiments on a complex real life prediction problem (entertainment video traffic) indicate that prior knowledge can be obtained through stochastic analysis both with respect to an appropriate NN architecture as well as to an appropriate sampling rate, in the case of a prediction horizon larger than one. An improvement of the obtained NN predictor is also proposed through a bias removal post-processing, resulting in much better performance than the best stochastic model.
Gene regulation and noise reduction by coupling of stochastic processes
Ramos, Alexandre F.; Hornos, José Eduardo M.; Reinitz, John
2015-02-01
Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.
Method for generating two coupled Gaussian stochastic processes
Jamali, Tayeb
2016-01-01
Most processes in nature are coupled; however, extensive null models for generating such processes still lacks. We present a new method to generate two coupled Gaussian stochastic processes with arbitrary correlation functions. This method is developed by modifying the Fourier filtering method. The robustness of this method is proved by generating two coupled fractional Brownian motions and extending its range of application to Gaussian random fields.
Granger causality and contiguity between stochastic processes
Energy Technology Data Exchange (ETDEWEB)
Triacca, Umberto [Universita di L' Aquila, Roio Poggio, I-67040 L' Aquila (Italy)]. E-mail: triacca@ec.univaq.it
2007-03-05
Although according to many econometricians the definition of causality proposed by Granger differs from other definitions of causation in the philosophy of science, in this Letter we argue that it is not completely lacking in philosophical legitimacy. We attempt to shed new light on the nexus between Granger causality and the concept of contiguity. In particular, we prove that the existence of a Granger causal link between two stochastic processes requires that these be 'contiguous' or that there exist a chain of processes, one contiguous to the next, which link the two processes.
Minimum uncertainty and squeezing in diffusion processes and stochastic quantization
Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe
1994-01-01
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
Option Pricing with Stochastic Volatility and Jump Diffusion Processes
Directory of Open Access Journals (Sweden)
Radu Lupu
2006-05-01
Full Text Available Option pricing by the use of Black Scholes Merton (BSM model is based on the assumption that asset prices have a lognormal distribution. In spite of the use of these models on a large scale, both by practioners and academics, the assumption of lognormality is rejected by the history of returns. The objective of this article is to present the methods that developed after the Black Scholes Merton environment and deals with the option pricing model adjustment to the empirical properties of asset returns. The main models that appeared after BSM allowed for special changes of the returns that materialized in jump-diffusion and stochastic volatility processes. The article presents the foundations of risk neutral options evaluation and the empirical evidence that fed the amendment of the lognormal assumption in the first part and shows the evaluation procedure under the assumption of stock prices following the jump-diffusion process and the stochastic volatility process.
Option Pricing with Stochastic Volatility and Jump Diffusion Processes
Directory of Open Access Journals (Sweden)
Radu Lupu
2006-03-01
Full Text Available Option pricing by the use of Black Scholes Merton (BSM model is based on the assumption that asset prices have a lognormal distribution. In spite of the use of these models on a large scale, both by practioners and academics, the assumption of lognormality is rejected by the history of returns. The objective of this article is to present the methods that developed after the Black Scholes Merton environment and deals with the option pricing model adjustment to the empirical properties of asset returns. The main models that appeared after BSM allowed for special changes of the returns that materialized in jump-diffusion and stochastic volatility processes. The article presents the foundations of risk neutral options evaluation and the empirical evidence that fed the amendment of the lognormal assumption in the first part and shows the evaluation procedure under the assumption of stock prices following the jump-diffusion process and the stochastic volatility process.
Stochastic Modelling and Analysis of Warehouse Operations
Y. Gong (Yeming)
2009-01-01
textabstractThis thesis has studied stochastic models and analysis of warehouse operations. After an overview of stochastic research in warehouse operations, we explore the following topics. Firstly, we search optimal batch sizes in a parallel-aisle warehouse with online order arrivals. We employ a
Simulating river meandering processes using stochastic bank erosion coefficient
Posner, Ari J.; Duan, Jennifer G.
2012-08-01
This study first compares the first order analytical solutions for flow field by Ikeda et. al. (1981) and Johanesson and Parker (1989b). Ikeda et. al.'s (1981) linear model of bank erosion was implemented to predict the rate of bank erosion in which the bank erosion coefficient is treated as a stochastic variable that varies with physical properties of the bank (e.g. cohesiveness, stratigraphy, vegetation density). The developed model was used to predict the evolution of meandering planforms. Then, the modeling results were analyzed and compared to the observed data. Because the migration of meandering channels consists of downstream translation, lateral expansion, and downstream or upstream rotations, several measures are formulated to determine which of the resulting planform is closest to the experimental measured one. Results from the deterministic model highly depend on the calibrated erosion coefficient. Because field measurements are always limited, the stochastic model yielded more realistic predictions of meandering planform evolutions. Because the coefficient of bank erosion is a random variable, the meandering planform evolution is a stochastic process that can only be accurately predicted by a stochastic model.
Normal forms for reduced stochastic climate models
Majda, A.J.; Franzke, C.; Crommelin, D.T.
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive highdimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from
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.
Introduction to Queueing Theory and Stochastic Teletraffic Models
Zukerman, Moshe
2013-01-01
The aim of this textbook is to provide students with basic knowledge of stochastic models that may apply to telecommunications research areas, such as traffic modelling, resource provisioning and traffic management. These study areas are often collectively called teletraffic. This book assumes prior knowledge of a programming language, mathematics, probability and stochastic processes normally taught in an electrical engineering course. For students who have some but not sufficiently strong b...
Karssenberg, D.J.; Schmitz, O.; Salamon, P.; Jong, K. de; Bierkens, M.F.P.
2010-01-01
Process-based spatio-temporal models simulate changes over time using equations that represent real world processes. They are widely applied in geography and earth science. Software implementation of the model itself and integrating model results with observations through data assimilation are two i
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
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...
Applications of Little's Law to stochastic models of gene expression
Elgart, Vlad; Kulkarni, Rahul V
2010-01-01
The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of mRNA fluctuations ('Poisson' and 'Telegraph' processes) have been proposed in stochastic models of gene expression. Both Poisson and Telegraph scenario models explain experimental observations of noise in protein levels in terms of 'bursts' of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The de...
Stochastic modeling 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 a physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficient D is strongly dependent on the w/c ratio and the temperature....... A deterministic relationship between the diffusion coefficient and the w/c ratio and the temperature is used for the stochastic modelling. The w/c ratio and the temperature are modelled by log-normally and normally distributed stochastic variables, respectively. It is then shown by Monte Carlo simulation...... that the diffusion coefficient D may be modelled by a normally distributed stochastic variable. The sensitivities of D with regard to the mean values and the standard deviations are evaluated....
Stochastic string models with continuous semimartingales
Bueno-Guerrero, Alberto; Moreno, Manuel; Navas, Javier F.
2015-09-01
This paper reformulates the stochastic string model of Santa-Clara and Sornette using stochastic calculus with continuous semimartingales. We present some new results, such as: (a) the dynamics of the short-term interest rate, (b) the PDE that must be satisfied by the bond price, and (c) an analytic expression for the price of a European bond call option. Additionally, we clarify some important features of the stochastic string model and show its relevance to price derivatives and the equivalence with an infinite dimensional HJM model to price European options.
Stochastic transition model for pedestrian dynamics
Schultz, Michael
2012-01-01
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion model is extended by both a grid-based path planning and mid-range agent interaction component. The stochastic model proves its capabilities for a quantitative reproduction of the characteristic shape of the common fundamental diagram of pedestrian dynamics. Moreover, effects of self-organizing behavior are successfully reproduced. The stochastic cellular automata approach is found to be adequate with respect to uncertainties in human motion patterns, a feature previously held by artificial noise terms alone.
Stochastic Control Model on Rent Seeking
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A continuous-time stochastic model is constructed to analyze how to control rent seeking behaviors. Using the stochastic optimization methods based on the modern risky theory, a unique positive solution to the dynamic model is derived. The effects of preference-related parameters on the optimal control level of rent seeking are discussed, and some policy measures are given. The results show that there exists a unique solution to the stochastic dynamic model under some macroeconomic assumptions, and that raising public expenditure may have reverse effects on rent seeking in an underdeveloped or developed economic environment.
Aerodynamic Noise Prediction Using stochastic Turbulence Modeling
Directory of Open Access Journals (Sweden)
Arash Ahmadzadegan
2008-01-01
Full Text Available Amongst many approaches to determine the sound propagated from turbulent flows, hybrid methods, in which the turbulent noise source field is computed or modeled separately from the far field calculation, are frequently used. For basic estimation of sound propagation, less computationally intensive methods can be developed using stochastic models of the turbulent fluctuations (turbulent noise source field. A simple and easy to use stochastic model for generating turbulent velocity fluctuations called continuous filter white noise (CFWN model was used. This method based on the use of classical Langevian-equation to model the details of fluctuating field superimposed on averaged computed quantities. The resulting sound field due to the generated unsteady flow field was evaluated using Lighthill's acoustic analogy. Volume integral method used for evaluating the acoustic analogy. This formulation presents an advantage, as it confers the possibility to determine separately the contribution of the different integral terms and also integration regions to the radiated acoustic pressure. Our results validated by comparing the directivity and the overall sound pressure level (OSPL magnitudes with the available experimental results. Numerical results showed reasonable agreement with the experiments, both in maximum directivity and magnitude of the OSPL. This method presents a very suitable tool for the noise calculation of different engineering problems in early stages of the design process where rough estimates using cheaper methods are needed for different geometries.
A Hierarchical Latent Stochastic Differential Equation Model for Affective Dynamics
Oravecz, Zita; Tuerlinckx, Francis; Vandekerckhove, Joachim
2011-01-01
In this article a continuous-time stochastic model (the Ornstein-Uhlenbeck process) is presented to model the perpetually altering states of the core affect, which is a 2-dimensional concept underlying all our affective experiences. The process model that we propose can account for the temporal changes in core affect on the latent level. The key…
Sanchez-Vila, X.; Fernàndez-Garcia, D.
2016-12-01
We address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology and numerical modeling have become routine in hydrogeological studies, nondeterministic models have not yet permeated into practitioners. We point out a number of limitations of stochastic modeling when applied to real applications and comment on the reasons why stochastic models fail to become an attractive alternative for practitioners. We specifically separate issues corresponding to flow, conservative transport, and reactive transport. The different topics addressed are emphasis on process modeling, need for upscaling parameters and governing equations, relevance of properly accounting for detailed geological architecture in hydrogeological modeling, and specific challenges of reactive transport. We end up by concluding that the main responsible for nondeterministic models having not yet permeated in industry can be fully attributed to researchers in stochastic hydrogeology.
Quantum Dynamics as a Stochastic Process
Figueiredo, J M A
2002-01-01
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model is obtained. The resulting theory is similar to Quantum Mechanics, having the same field equations for probability measures, the same operator structure and symmetric ordering of operators. The model is valid for general electromagnetic interaction as well as many body systems with mutual interactions of general nature.
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.
Analysis of bilinear stochastic systems. [involving multiplicative noise processes
Willsky, A. S.; Marcus, S. I.; Martin, D. N.
1974-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Stochastic multiscale modeling of polycrystalline materials
Wen, Bin
provides a new outlook to multi-scale materials modeling accounting for microstructure and process uncertainties. Predictive materials modeling will accelerate the development of new materials and processes for critical applications in industry.
Population Density Equations for Stochastic Processes with Memory Kernels
Lai, Yi Ming
2016-01-01
We present a novel method for solving population density equations, where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. There are important advantages over earlier methods: instead of introducing an extra dimension, we find that the history of the noise process can always be accounted for by the convolution of a kernel of limited depth with a history of the density, rendering the method more efficient. Excitatory and inhibitory input contributions can be treated on equal footing. Transient results can be modeled accurately, which is of vital importance as population density methods are increasingly used to model neural circuits. This method can be used in network simulations where analytic results are not available. The method cleanly separates deterministic and stochastic processes, leaving only the evolution of the stochastic process to be solved. This allows for a direct incorporation of novel developments in the theory of random walks. We demonstrate this by...
Stationary stochastic processes for scientists and engineers
Lindgren, Georg; Sandsten, Maria
2013-01-01
""This book is designed for a first course in stationary stochastic processes in science and engineering and does a very good job in introducing many concepts and ideas to students in these fields. … the book has probably been tested in the classroom many times, which also manifests itself in its virtual lack of typos. … Another great feature of the book is that it contains a wealth of worked example from many different fields. These help clarify concepts and theorems and I believe students will appreciate them-I certainly did. … The book is well suited for a one-semester course as it contains
A first course in stochastic processes
Karlin, Samuel
1975-01-01
The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other.The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processe
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......A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered...... 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...
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique...... applied for implementing this semantics in the UPPAAL-SMC simulation engine. We report on two applications of the resulting tool-set coming from systems biology and energy aware buildings....
Second Quantization Approach to Stochastic Epidemic Models
Mondaini, Leonardo
2015-01-01
We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of closed master equations describing the population dynamics of multivariate stochastic epidemic models. In order to do that, we introduce an SIR-inspired stochastic model for hepatitis C virus epidemic, from which we obtain the time evolution of the mean number of susceptible, infected, recovered and chronically infected individuals in a population whose total size is allowed to change.
Deterministic versus stochastic aspects of superexponential population growth models
Grosjean, Nicolas; Huillet, Thierry
2016-08-01
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a much richer variety of behaviors. One is the Lamperti construction of selfsimilar positive stochastic processes based on the exponentiation of spectrally positive processes, followed by an appropriate time change. The other one is based on stable continuous-state branching processes, given by another Lamperti time substitution applied to stable spectrally positive processes.
A Stochastic Energy Budget Model Using Physically Based Red Noise
Weniger, Michael; Hense, Andreas
2011-01-01
A method to describe unresolved processes in meteorological models by physically based stochastic processes (SP) is proposed by the example of an energy budget model (EBM). Contrary to the common approach using additive white noise, a suitable variable within the model is chosen to be represented by a SP. Spectral analysis of ice core time series shows a red noise character of the underlying fluctuations. Fitting Ornstein Uhlenbeck processes to the observed spectrum defines the parameters for the stochastic dynamic model (SDM). Numerical simulations for different sets of ice core data lead to three sets of strongly differing systems. Pathwise, statistical and spectral analysis of these models show the importance of carefully choosing suitable stochastic terms in order to get a physically meaningful SDM.
Dynamics of a Stochastic Intraguild Predation Model
Directory of Open Access Journals (Sweden)
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.
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...... 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...... 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...
XI Symposium on Probability and Stochastic Processes
Pardo, Juan; Rivero, Víctor; Bravo, Gerónimo
2015-01-01
This volume features lecture notes and a collection of contributed articles from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since the symposium was part of the activities organized in Mexico to celebrate the International Year of Statistics, the program included topics from the interface between statistics and stochastic processes. The book starts with notes from the mini-course given by Louigi Addario-Berry with an accessible description of some features of the multiplicative coalescent and its connection with random graphs and minimum spanning trees. It includes a number of exercises and a section on unanswered questions. Further contributions provide the reader with a broad perspective on the state-of-the art of active areas of research. Contributions by: Louigi Addario-Berry Octavio Arizmendi Fabrice Baudoin Jochen Blath Loïc Chaumont J. Armando Domínguez-Molina Bjarki Eldon Shui Feng Tulio Gaxiola Adrián González Casanova Evgueni Gordienko Daniel...
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-01
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.
Multivariate moment closure techniques for stochastic kinetic models.
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D W; Stumpf, Michael P H
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.
Stochasticity in processes fundamentals and applications to chemistry and biology
Schuster, Peter
2016-01-01
This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic collection of the mathematical background material needed to understand probability, statistics, and stochastic processes as a prerequisite for the increasingly challenging practical applications in chemistry and the life sciences examined in the second part. Recent advances in the development of new techniques and in the resolution of conventional experiments at nano-scales have been tremendous: today molecular spectroscopy can provide insights into processes down to scales at which current theories at the interface of physics, chemistry and the life sciences cannot be successful without a firm grasp of randomness and its sources. Routinely measured data is now sufficiently accurate to allow the direct recording of fluctuations. As a result, the sampling of data and the modeling of relevant processes are doomed t...
Model checking mobile stochastic logic.
De Nicola, Rocco; Katoen, Joost P.; Latella, Diego; Loreti, Michele; Massink, Mieke
2007-01-01
The Temporal Mobile Stochastic Logic (MOSL) has been introduced in previous work by the authors for formulating properties of systems specified in STOKLAIM, a Markovian extension of KLAIM. The main purpose of MOSL is to address key functional aspects of global computing such as distribution
Model checking mobile stochastic logic.
De Nicola, Rocco; Katoen, Joost-Pieter; Latella, Diego; Loreti, Michele; Massink, Mieke
2007-01-01
The Temporal Mobile Stochastic Logic (MOSL) has been introduced in previous work by the authors for formulating properties of systems specified in STOKLAIM, a Markovian extension of KLAIM. The main purpose of MOSL is to address key functional aspects of global computing such as distribution awarenes
GEMFsim: A Stochastic Simulator for the Generalized Epidemic Modeling Framework
Sahneh, Faryad Darabi; Shakeri, Heman; Fan, Futing; Scoglio, Caterina
2016-01-01
The recently proposed generalized epidemic modeling framework (GEMF) \\cite{sahneh2013generalized} lays the groundwork for systematically constructing a broad spectrum of stochastic spreading processes over complex networks. This article builds an algorithm for exact, continuous-time numerical simulation of GEMF-based processes. Moreover the implementation of this algorithm, GEMFsim, is available in popular scientific programming platforms such as MATLAB, R, Python, and C; GEMFsim facilitates simulating stochastic spreading models that fit in GEMF framework. Using these simulations one can examine the accuracy of mean-field-type approximations that are commonly used for analytical study of spreading processes on complex networks.
Models and Algorithm for Stochastic Network Designs
Institute of Scientific and Technical Information of China (English)
Anthony Chen; Juyoung Kim; Seungjae Lee; Jaisung Choi
2009-01-01
The network design problem (NDP) is one of the most difficult and challenging problems in trans-portation. Traditional NDP models are often posed as a deterministic bilevel program assuming that all rele-vant inputs are known with certainty. This paper presents three stochastic models for designing transporta-tion networks with demand uncertainty. These three stochastic NDP models were formulated as the ex-pected value model, chance-constrained model, and dependent-chance model in a bilevel programming framework using different criteria to hedge against demand uncertainty. Solution procedures based on the traffic assignment algorithm, genetic algorithm, and Monte-Cado simulations were developed to solve these stochastic NDP models. The nonlinear and nonconvex nature of the bilevel program was handled by the genetic algorithm and traffic assignment algorithm, whereas the stochastic nature was addressed through simulations. Numerical experiments were conducted to evaluate the applicability of the stochastic NDP models and the solution procedure. Results from the three experiments show that the solution procedures are quite robust to different parameter settings.
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 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 P systems and the simulation of biochemical processes with dynamic compartments.
Spicher, Antoine; Michel, Olivier; Cieslak, Mikolaj; Giavitto, Jean-Louis; Prusinkiewicz, Przemyslaw
2008-03-01
We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.
A Novel Formal Analysis Method of Network Survivability Based on Stochastic Process Algebra
Institute of Scientific and Technical Information of China (English)
ZHAO Guosheng; WANG Huiqiang; WANG Jian
2007-01-01
Stochastic process algebras have been proposed as compositional specification formalisms for performance models. A formal analysis method of survivable network was proposed based on stochastic process algebra, which incorporates formal modeling into performance analysis perfectly, and then various performance parameters of survivable network can be simultaneously obtained after formal modeling. The formal description with process expression to the survivable network system was carried out based on the simply introduced syntax and operational semantics of stochastic process algebra. Then PEPA workbench tool was used to obtain the probability of system's steady state availability and transient state availability. Simulation experiments show the effectiveness and feasibility of the developed method.
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.
A Stochastic Skeleton Model for the MJO
Stechmann, S. N.; Thual, S.; Majda, A.
2014-12-01
The Madden-Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal time scales and planetary spatial scales. Despite the primary importance of the MJO and the decades of research progress since its original discovery, a generally accepted theory for its essential mechanisms has remained elusive. In recent work by two of the authors, a minimal dynamical model has been proposed that recovers robustly the most fundamental MJO features of (i) a slow eastward speed of roughly 5 m/s, (ii) a peculiar dispersion relation with dω/dk≈0, and (iii) a horizontal quadrupole vortex structure. This model, the skeleton model, depicts the MJO as a neutrally stable atmospheric wave that involves a simple multiscale interaction between planetary dry dynamics, planetary lower-tropospheric moisture, and the planetary envelope of synoptic-scale activity. In this article, it is shown that the skeleton model can further account for (iv) the intermittent generation of MJO events and (v) the organization of MJO events into wave trains with growth and demise, as seen in nature. The goal is achieved by developing a simple stochastic parameterization for the unresolved details of synoptic-scale activity, which is coupled to otherwise deterministic processes in the skeleton model. In particular, the intermittent initiation, propagation, and shut down of MJO wave trains in the skeleton model occur through these stochastic effects. This includes examples with a background warm pool where some initial MJO-like disturbances propagate through the western region but stall at the peak of background convection/heating corresponding to the Maritime Continent in nature. Also shown are examples with an idealized seasonal cycle, namely a background warm pool state of heating/moistening displacing meridionally during the year. This seasonally varying case considers both equatorial and off-equatorial components of the envelope of synoptic scale convective
Stochastic processes dominate during boreal bryophyte community assembly.
Fenton, Nicole J; Bergeron, Yves
2013-09-01
Why are plant species found in certain locations and not in others? The study of community assembly rules has attempted to answer this question, and many studies articulate the historic dichotomy of deterministic (predictable niches) vs. stochastic (random or semi-random processes). The study of successional sequences to determine whether they converge, as would be expected by deterministic theory, or diverge, as stochastic theory would suggest, has been one method used to investigate this question. In this article we ask the question: Do similar boreal bryophyte communities develop in the similar habitat created by convergent succession after fires of different severities? Or do the stochastic processes generated by fires of different severity lead to different communities? Specifically we predict that deterministic structure will be more important for large forest-floor species than stochastic processes, and that the inverse will be true for small bryophyte species. We used multivariate regression trees and model selection to determine the relative weight of structure (forest structure, substrates, soil structure) and processes (fire severity) for two groups of bryophyte species sampled in 12 sites (seven high-severity and five low-severity fires). Contrary to our first hypothesis, processes were as important for large forest-floor bryophytes as for small pocket species. Fire severity, its interaction with the quality of available habitat, and its impact on the creation of biological legacies played dominant roles in determining community structure. In this study, sites with nearly identical forest structure, generated via convergent succession after high- and low-severity fire, were compared to see whether these sites supported similar bryophyte communities. While similar to some degree, both the large forest-floor species and the pocket species differed after high-severity fire compared to low-severity fire. This result suggests that the "how," or process of
An introduction to stochastic processes with applications to biology
Allen, Linda J S
2010-01-01
An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and the genetics of inbreeding. Because of their rich structure, the text focuses on discrete and continuous time Markov chains and continuous time and state Markov processes.New to the Second EditionA new chapter on stochastic differential equations th
Applied probability and stochastic processes. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Feldman, Richard M. [Texas A and M Univ., College Station, TX (United States). Industrial and Systems Engineering Dept.; Valdez-Flores, Ciriaco [Sielken and Associates Consulting, Inc., Bryan, TX (United States)
2010-07-01
This book presents applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications of the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. The initial chapters present a summary of probability and statistics and then Poisson processes, Markov chains, Markov processes and queuing processes are introduced. Advanced topics include simulation, inventory theory, replacement theory, Markov decision theory, and the use of matrix geometric procedures in the analysis of queues. Included in the second edition are appendices at the end of several chapters giving suggestions for the use of Excel in solving the problems of the chapter. Also new in this edition are an introductory chapter on statistics and a chapter on Poisson processes that includes some techniques used in risk assessment. The old chapter on queues has been expanded and broken into two new chapters: one for simple queuing processes and one for queuing networks. Support is provided through the web site http://apsp.tamu.edu where students will have the answers to odd numbered problems and instructors will have access to full solutions and Excel files for homework. (orig.)
The multivariate supOU stochastic volatility model
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Stelzer, Robert
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......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...
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 inverse problems: Models and metrics
Energy Technology Data Exchange (ETDEWEB)
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim [Victor Technologies, LLC, Bloomington, IN 47407-7706 (United States); Aldrin, John C. [Computational Tools, Gurnee, IL 60031 (United States); Annis, Charles [Statistical Engineering, Palm Beach Gardens, FL 33418 (United States); Knopp, Jeremy S. [Air Force Research Laboratory (AFRL/RXCA), Wright Patterson AFB, OH 45433-7817 (United States)
2015-03-31
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.
Level Crossing Methods in Stochastic Models
Brill, Percy H
2008-01-01
Since its inception in 1974, the level crossing approach for analyzing a large class of stochastic models has become increasingly popular among researchers. This volume traces the evolution of level crossing theory for obtaining probability distributions of state variables and demonstrates solution methods in a variety of stochastic models including: queues, inventories, dams, renewal models, counter models, pharmacokinetics, and the natural sciences. Results for both steady-state and transient distributions are given, and numerous examples help the reader apply the method to solve problems fa
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Directory of Open Access Journals (Sweden)
Slawomir Antoni Lux
2016-08-01
Full Text Available The paper reports application of a Markov-like stochastic process agent-based model and a ‘virtual farm’ concept for enhancement of site-specific Integrated Pest Management. Conceptually, the model represents a ‘bottom-up ethological’ approach and emulates behaviour of the ‘primary IPM actors’ - large cohorts of individual insects - within seasonally changing mosaics of spatiotemporally complex faming landscape, under the challenge of the local IPM actions. Algorithms of the proprietary PESTonFARM model were adjusted to reflect behaviour and ecology of R. cerasi. Model parametrization was based on compiled published information about R. cerasi and the results of auxiliary on-farm experiments. The experiments were conducted on sweet cherry farms located in Austria, Germany and Belgium. For each farm, a customised model-module was prepared, reflecting its spatiotemporal features. Historical data about pest monitoring, IPM treatments and fruit infestation were used to specify the model assumptions and calibrate it further. Finally, for each of the farms, virtual IPM experiments were simulated and the model-generated results were compared with the results of the real experiments conducted on the same farms. Implications of the findings for broader applicability of the model and the ‘virtual farm’ approach - were discussed.
Lux, Slawomir A; Wnuk, Andrzej; Vogt, Heidrun; Belien, Tim; Spornberger, Andreas; Studnicki, Marcin
2016-01-01
The paper reports application of a Markov-like stochastic process agent-based model and a "virtual farm" concept for enhancement of site-specific Integrated Pest Management. Conceptually, the model represents a "bottom-up ethological" approach and emulates behavior of the "primary IPM actors"-large cohorts of individual insects-within seasonally changing mosaics of spatiotemporally complex faming landscape, under the challenge of the local IPM actions. Algorithms of the proprietary PESTonFARM model were adjusted to reflect behavior and ecology of R. cerasi. Model parametrization was based on compiled published information about R. cerasi and the results of auxiliary on-farm experiments. The experiments were conducted on sweet cherry farms located in Austria, Germany, and Belgium. For each farm, a customized model-module was prepared, reflecting its spatiotemporal features. Historical data about pest monitoring, IPM treatments and fruit infestation were used to specify the model assumptions and calibrate it further. Finally, for each of the farms, virtual IPM experiments were simulated and the model-generated results were compared with the results of the real experiments conducted on the same farms. Implications of the findings for broader applicability of the model and the "virtual farm" approach-were discussed.
From cusps to cores: a stochastic model
El-Zant, Amr A.; Freundlich, Jonathan; Combes, Françoise
2016-09-01
The cold dark matter model of structure formation faces apparent problems on galactic scales. Several threads point to excessive halo concentration, including central densities that rise too steeply with decreasing radius. Yet, random fluctuations in the gaseous component can `heat' the centres of haloes, decreasing their densities. We present a theoretical model deriving this effect from first principles: stochastic variations in the gas density are converted into potential fluctuations that act on the dark matter; the associated force correlation function is calculated and the corresponding stochastic equation solved. Assuming a power-law spectrum of fluctuations with maximal and minimal cutoff scales, we derive the velocity dispersion imparted to the halo particles and the relevant relaxation time. We further perform numerical simulations, with fluctuations realized as a Gaussian random field, which confirm the formation of a core within a time-scale comparable to that derived analytically. Non-radial collective modes enhance the energy transport process that erases the cusp, though the parametrizations of the analytical model persist. In our model, the dominant contribution to the dynamical coupling driving the cusp-core transformation comes from the largest scale fluctuations. Yet, the efficiency of the transformation is independent of the value of the largest scale and depends weakly (linearly) on the power-law exponent; it effectively depends on two parameters: the gas mass fraction and the normalization of the power spectrum. This suggests that cusp-core transformations observed in hydrodynamic simulations of galaxy formation may be understood and parametrized in simple terms, the physical and numerical complexities of the various implementations notwithstanding.
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....
Analysing Social Epidemics by Delayed Stochastic Models
Directory of Open Access Journals (Sweden)
Francisco-José Santonja
2012-01-01
Full Text Available We investigate the dynamics of a delayed stochastic mathematical model to understand the evolution of the alcohol consumption in Spain. Sufficient condition for stability in probability of the equilibrium point of the dynamic model with aftereffect and stochastic perturbations is obtained via Kolmanovskii and Shaikhet general method of Lyapunov functionals construction. We conclude that alcohol consumption in Spain will be constant (with stability in time with around 36.47% of nonconsumers, 62.94% of nonrisk consumers, and 0.59% of risk consumers. This approach allows us to emphasize the possibilities of the dynamical models in order to study human behaviour.
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.
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.
Impacts of Stochastic Modeling on GPS-derived ZTD Estimations
Jin, Shuanggen
2010-01-01
GPS-derived ZTD (Zenith Tropospheric Delay) plays a key role in near real-time weather forecasting, especially in improving the precision of Numerical Weather Prediction (NWP) models. The ZTD is usually estimated using the first-order Gauss-Markov process with a fairly large correlation, and under the assumption that all the GPS measurements, carrier phases or pseudo-ranges, have the same accuracy. However, these assumptions are unrealistic. This paper aims to investigate the impact of several stochastic modeling methods on GPS-derived ZTD estimations using Australian IGS data. The results show that the accuracy of GPS-derived ZTD can be improved using a suitable stochastic model for the GPS measurements. The stochastic model using satellite elevation angle-based cosine function is better than other investigated stochastic models. It is noted that, when different stochastic modeling strategies are used, the variations in estimated ZTD can reach as much as 1cm. This improvement of ZTD estimation is certainly c...
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.
Directory of Open Access Journals (Sweden)
Christley Scott
2010-07-01
Full Text Available Abstract Background Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species. Results We propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD. We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC, and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models. Conclusions The SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is
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...
Nonlinear stochastic inflation modelling using SEASETARs
de Gooijer, J.G.; Vidiella-i-Anguera, A.
2003-01-01
The development of stochastic inflation models for actuarial and investment applications has become an important topic to actuaries since Wilkie [Transactions of the Faculty of Actuaries 39 (1986) 341] introduced his first investment model. Two empirical features of monthly inflation rates are dynam
Regulation mechanisms in spatial stochastic development models
Finkelshtein, Dmitri
2008-01-01
The aim of this paper is to analyze different regulation mechanisms in spatial continuous stochastic development models. We describe the density behavior for models with global mortality and local establishment rates. We prove that the local self-regulation via a competition mechanism (density dependent mortality) may suppress a unbounded growth of the averaged density if the competition kernel is superstable.
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 s...... as it pinpoints which decisions to be concerned about when the goal is to predict footbridge response. The studies involve estimating footbridge responses using Monte-Carlo simulations and focus is on estimating vertical structural response to single person loading....
Modeling stochasticity in biochemical reaction networks
Constantino, P. H.; Vlysidis, M.; Smadbeck, P.; Kaznessis, Y. N.
2016-03-01
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.
Multiple-scale stochastic processes: Decimation, averaging and beyond
Bo, Stefano; Celani, Antonio
2017-02-01
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This has provided fruitful applications for established stochastic methods and motivated further developments. These systems often involve processes taking place on widely separated time scales. For an efficient modeling one usually focuses on the slower degrees of freedom and it is of great importance to accurately eliminate the fast variables in a controlled fashion, carefully accounting for their net effect on the slower dynamics. This procedure in general requires to perform two different operations: decimation and coarse-graining. We introduce the asymptotic methods that form the basis of this procedure and discuss their application to a series of physical, biological and chemical examples. We then turn our attention to functionals of the stochastic trajectories such as residence times, counting statistics, fluxes, entropy production, etc. which have been increasingly studied in recent years. For such functionals, the elimination of the fast degrees of freedom can present additional difficulties and naive procedures can lead to blatantly inconsistent results. Homogenization techniques for functionals are less covered in the literature and we will pedagogically present them here, as natural extensions of the ones employed for the trajectories. We will also discuss recent applications of these techniques to the thermodynamics of small systems and their interpretation in terms of information-theoretic concepts.
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 differential equations and diffusion processes
Ikeda, N
1989-01-01
Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sectio
Stochastic spatial models of plant diseases
Brown, D H
2001-01-01
I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of timescales argument to determine the effects of spatial clustering on threshold structure. By computing the spatial structure early in an invasion, I find explicit corrections to mean field theory. In the first chapter, I present a lattice model of a disease that is not directly lethal to its host, but affects its ability to compete with neighbors. I use a type of pair approximation to determine conditions for invasions and coexistence. In the second chapter, I study a basic SIR epidemic point process in continuous space. I implement a multiplicative moment closure scheme to compute the threshold transmission rate as a function of spatial parameters. In the final chapter, I model the evolution of pathogen resistance when two plant species share a pathogen. Evolution may lead...
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...
Time Reversal of Volterra Processes Driven Stochastic Differential Equations
Directory of Open Access Journals (Sweden)
L. Decreusefond
2013-01-01
Full Text Available We consider stochastic differential equations driven by some Volterra processes. Under time reversal, these equations are transformed into past-dependent stochastic differential equations driven by a standard Brownian motion. We are then in position to derive existence and uniqueness of solutions of the Volterra driven SDE considered at the beginning.
Vaccination Control in a Stochastic SVIR Epidemic Model.
Witbooi, Peter J; Muller, Grant E; Van Schalkwyk, Garth J
2015-01-01
For a stochastic differential equation SVIR epidemic model with vaccination, we prove almost sure exponential stability of the disease-free equilibrium for ℛ(0) stochastic model as well as for the underlying deterministic model. In order to solve the stochastic problem numerically, we use an approximation based on the solution of the deterministic model.
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
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 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
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 for
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
A stochastic model for bacteriophage therapies
Bardina, Xavier; Rovira, Carles; Tindel, Samy
2011-01-01
In this article, we analyze a system modeling bacteriophage treatments for infections in a noisy context. In the small noise regime, we show that after a reasonable amount of time the system is close to a sane equilibrium (which is a relevant biologic information) with high probability. Mathematically speaking, our study hinges on concentration techniques for delayed stochastic differential equations.
Stochastic models of intracellular calcium signals
Energy Technology Data Exchange (ETDEWEB)
Rüdiger, Sten, E-mail: sten.ruediger@physik.hu-berlin.de
2014-01-10
Cellular signaling operates in a noisy environment shaped by low molecular concentrations and cellular heterogeneity. For calcium release through intracellular channels–one of the most important cellular signaling mechanisms–feedback by liberated calcium endows fluctuations with critical functions in signal generation and formation. In this review it is first described, under which general conditions the environment makes stochasticity relevant, and which conditions allow approximating or deterministic equations. This analysis provides a framework, in which one can deduce an efficient hybrid description combining stochastic and deterministic evolution laws. Within the hybrid approach, Markov chains model gating of channels, while the concentrations of calcium and calcium binding molecules (buffers) are described by reaction–diffusion equations. The article further focuses on the spatial representation of subcellular calcium domains related to intracellular calcium channels. It presents analysis for single channels and clusters of channels and reviews the effects of buffers on the calcium release. For clustered channels, we discuss the application and validity of coarse-graining as well as approaches based on continuous gating variables (Fokker–Planck and chemical Langevin equations). Comparison with recent experiments substantiates the stochastic and spatial approach, identifies minimal requirements for a realistic modeling, and facilitates an understanding of collective channel behavior. At the end of the review, implications of stochastic and local modeling for the generation and properties of cell-wide release and the integration of calcium dynamics into cellular signaling models are discussed.
A Stochastic Dynamic Model of Computer Viruses
Directory of Open Access Journals (Sweden)
Chunming Zhang
2012-01-01
Full Text Available A stochastic computer virus spread model is proposed and its dynamic behavior is fully investigated. Specifically, we prove the existence and uniqueness of positive solutions, and the stability of the virus-free equilibrium and viral equilibrium by constructing Lyapunov functions and applying Ito's formula. Some numerical simulations are finally given to illustrate our main results.
Stochastic Modeling of Airlines' Scheduled Services Revenue
Hamed, M. M.
1999-01-01
Airlines' revenue generated from scheduled services account for the major share in the total revenue. As such, predicting airlines' total scheduled services revenue is of great importance both to the governments (in case of national airlines) and private airlines. This importance stems from the need to formulate future airline strategic management policies, determine government subsidy levels, and formulate governmental air transportation policies. The prediction of the airlines' total scheduled services revenue is dealt with in this paper. Four key components of airline's scheduled services are considered. These include revenues generated from passenger, cargo, mail, and excess baggage. By addressing the revenue generated from each schedule service separately, air transportation planners and designers are able to enhance their ability to formulate specific strategies for each component. Estimation results clearly indicate that the four stochastic processes (scheduled services components) are represented by different Box-Jenkins ARIMA models. The results demonstrate the appropriateness of the developed models and their ability to provide air transportation planners with future information vital to the planning and design processes.
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......, Phys. Rev. E 83, 016107 (2011)] incorporates a node degree correction to model degree heterogeneity within each group. Although this demonstrably leads to better performance on several networks, it is not obvious whether modeling node degree is always appropriate or necessary. We formulate the degree...... 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...
Introduction to probability and stochastic processes with applications
Castañ, Blanco; Arunachalam, Viswanathan; Dharmaraja, Selvamuthu
2012-01-01
An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic t
Extreme Values of Queues, Point Processes and Stochastic Networks.
2014-09-26
AD-A158 619 EXTREMIE YALUES OF QUEUES POINT PROCESSES AND STOCHASTIC i/i NETUORKS(U) GEORGIA INST OF TECH ATLANTA R F SERFOZO 25 JUN 85 SFOSR-TR-85...O If "Extreme Values of Queues, Point Processes VW- and Stochastic Networks" 1 Grant No. AFOSR 84-0367 by Professor Richard F. Serfozo Industrial and...Claaraicajton) Extreme Values of Oueues. Point Processes & Stochastic Networks_ 12. PERSONAL AUTHOR(S) R_ F_ Serfozo 13. TYPE OF REPORT 13b. TIME COVERED 14
Numerical solution of stochastic SIR model by Bernstein polynomials
Directory of Open Access Journals (Sweden)
N. Rahmani
2016-01-01
Full Text Available In this paper, we present numerical method based on Bernstein polynomials for solving the stochastic SIR model. By use of Bernstein operational matrix and its stochastic operational matrix we convert stochastic SIR model to a nonlinear system that can be solved by Newton method. Finally, a test problem of SIR model is presented to illustrate our mathematical findings.
Stochastic contribution to the growth factor in the LCDM model
Energy Technology Data Exchange (ETDEWEB)
Ribeiro, A. L.B.; Andrade, A. P.A.; Letelier, P. S.
2009-01-01
We study the effect of noise on the evolution of the growth factor of density perturbations in the context of the LCDM model. Stochasticity is introduced as a Wiener process amplified by an intensity parameter alpha. By comparing the evolution of deterministic and stochastic cases for different values of alpha we estimate the intensity level necessary to make noise relevant for cosmological tests based on large-scale structure data. Our results indicate that the presence of random forces underlying the fluid description can lead to significant deviations from the nonstochastic solution at late times for alpha>0.001.
Dynamical Monte Carlo method for stochastic epidemic models
Aiello, O E
2002-01-01
A new approach to Dynamical Monte Carlo Methods is introduced to simulate markovian processes. We apply this approach to formulate and study an epidemic Generalized SIRS model. The results are in excellent agreement with the forth order Runge-Kutta method in a region of deterministic solution. Introducing local stochastic interactions, the Runge-Kutta method is not applicable, and we solve and check it self-consistently with a stochastic version of the Euler Method. The results are also analyzed under the herd-immunity concept.
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...
A stochastic model of a cell population with quiescence.
Olofsson, Peter
2008-10-01
A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.
INTRUSION DETECTION BASED ON THE SECOND-ORDER STOCHASTIC MODEL
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper presents a new method based on a second-order stochastic model for computer intrusion detection. The results show that the performance of the second-order stochastic model is better than that of a first-order stochastic model. In this study, different window sizes are also used to test the performance of the model. The detection results show that the second-order stochastic model is not so sensitive to the window size, comparing with the first-order stochastic model and other previous researches. The detection result of window sizes 6 and 10 is the same.
Stochastic models for inferring genetic regulation from microarray gene expression data.
Tian, Tianhai
2010-03-01
Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information.
Stochastic resonance in a financial model
Institute of Scientific and Technical Information of China (English)
毛晓明; 孙锴; 欧阳颀
2002-01-01
We report on our model study of stochastic resonance in the stock market using numerical simulation and analysis.In the model, we take the interest rate as the external signal, the randomness of traders' behaviour as the noise, andthe stock price as the output. With computer simulations, we find that the system demonstrates a characteristic ofstochastic resonance as noise intensity varies. An analytical explanation is proposed.
Modelling Coagulation Systems: A Stochastic Approach
Ryazanov, V V
2011-01-01
A general stochastic approach to the description of coagulating aerosol system is developed. As the object of description one can consider arbitrary mesoscopic values (number of aerosol clusters, their size etc). The birth-and-death formalism for a number of clusters can be regarded as a partial case of the generalized storage model. An application of the storage model to the number of monomers in a cluster is discussed.
Stochastic modeling and performance monitoring of wind farm power production
Milan, Patrick; Peinke, Joachim
2015-01-01
We present a new stochastic approach to describe and remodel the conversion process of a wind farm at a sampling frequency of 1Hz. When conditioning on various wind direction sectors, the dynamics of the conversion process appear as a fluctuating trajectory around an average IEC-like power curve, see section II. Our approach is to consider the wind farm as a dynamical system that can be described as a stochastic drift/diffusion model, where a drift coefficient describes the attraction towards the power curve and a diffusion coefficient quantifies additional turbulent fluctuations. These stochastic coefficients are inserted into a Langevin equation that, once properly adapted to our particular system, models a synthetic signal of power output for any given wind speed/direction signals, see section III. When combined with a pre-model for turbulent wind fluctuations, the stochastic approach models the power output of the wind farm at a sampling frequency of 1Hz using only ten-minute average values of wind speed ...
Stochastic Flocculation Model for Cohesive Sediment Suspended in Water
Directory of Open Access Journals (Sweden)
Hyun Jung Shin
2015-05-01
Full Text Available Existing flocculation models for cohesive sediments are classified into two groups: population balance equation models (PBE and floc growth models. An FGM ensures mass conservation in a closed system. However, an FGM determines only the average size of flocs, whereas a PBE has the capability to calculate a size distribution of flocs. A new stochastic approach to model the flocculation process is theoretically developed and incorporated into a deterministic FGM in this study in order to calculate a size distribution of flocs as well as the average size. A log-normal distribution is used to generate random numbers based on previous laboratory experiments. The new stochastic flocculation model is tested with three laboratory experiment results. It was found and validated with measured data that the new stochastic flocculation model has the capability to replicate a size distribution of flocs reasonably well under different sediment and carrier flow conditions. Three more distributions (normal; Pearson type 3; and generalized extreme value distributions were also tested. From the comparison with results of different distribution functions, it is shown that a stochastic FGM using a log-normal distribution has a comparative advantage in terms of simplicity and accuracy.
Representation Theorems for Fuzzy Random Sets and Fuzzy Stochastic Processes
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set-valued random sets, fuzzy random elements and fuzzy set-valued stochastic processes are obtained.
Stochastic models for atomic clocks
Barnes, J. A.; Jones, R. H.; Tryon, P. V.; Allan, D. W.
1983-01-01
For the atomic clocks used in the National Bureau of Standards Time Scales, an adequate model is the superposition of white FM, random walk FM, and linear frequency drift for times longer than about one minute. The model was tested on several clocks using maximum likelihood techniques for parameter estimation and the residuals were acceptably random. Conventional diagnostics indicate that additional model elements contribute no significant improvement to the model even at the expense of the added model complexity.
Yashchuk, Valeriy V.; Tyurin, Yury N.; Tyurina, Anastasia Y.
2016-07-01
The design and evaluation of the expected performance of optical systems requires sophisticated and reliable information about the surface topography of planned optical elements before they are fabricated. The problem is especially severe in the case of x-ray optics for modern diffraction-limited-electron-ring and free-electron-laser x-ray facilities, as well as x-ray astrophysics missions, such as the X-ray Surveyor under development. Modern x-ray source facilities are reliant upon the availability of optics of unprecedented quality, with surface slope accuracy x-ray space observatories require high-quality optics of 100 m2 in total area. The uniqueness of the optics and limited number of proficient vendors make the fabrication extremely time-consuming and expensive, mostly due to the limitations in accuracy and measurement rate of metrology used in fabrication. We continue investigating the possibility of improving metrology efficiency via comprehensive statistical treatment of a compact volume of metrology of surface topography, which is considered the result of a stochastic polishing process. We suggest, verify, and discuss an analytical algorithm for identification of an optimal symmetric time-invariant linear filter model with a minimum number of parameters and smallest residual error. If successful, the modeling could provide feedback to deterministic polishing processes, avoiding time-consuming, whole-scale metrology measurements over the entire optical surface with the resolution required to cover the entire desired spatial frequency range. The modeling also allows forecasting of metrology data for optics made by the same vendor and technology. The forecast data are vital for reliable specification for optical fabrication, evaluated from numerical simulation to be exactly adequate for the required system performance, avoiding both over- and underspecification.
The Stochastic Modelling of Endemic Diseases
Susvitasari, Kurnia; Siswantining, Titin
2017-01-01
A study about epidemic has been conducted since a long time ago, but genuine progress was hardly forthcoming until the end of the 19th century (Bailey, 1975). Both deterministic and stochastic models were used to describe these. Then, from 1927 to 1939 Kermack and McKendrick introduced a generality of this model, including some variables to consider such as rate of infection and recovery. The purpose of this project is to investigate the behaviour of the models when we set the basic reproduction number, R0. This quantity is defined as the expected number of contacts made by a typical infective to susceptibles in the population. According to the epidemic threshold theory, when R0 ≤ 1, minor epidemic occurs with probability one in both approaches, but when R0 > 1, the deterministic and stochastic models have different interpretation. In the deterministic approach, major epidemic occurs with probability one when R0 > 1 and predicts that the disease will settle down to an endemic equilibrium. Stochastic models, on the other hand, identify that the minor epidemic can possibly occur. If it does, then the epidemic will die out quickly. Moreover, if we let the population size be large and the major epidemic occurs, then it will take off and then reach the endemic level and move randomly around the deterministic’s equilibrium.
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 particle based models for suspended particle movement in surface flows
Institute of Scientific and Technical Information of China (English)
Christina W.TSAI; Chuanjian MAN; Jungsun OH
2014-01-01
Modeling of suspended sediment particle movement in surface water can be achieved by stochastic particle tracking model approaches. In this paper, different mathematical forms of particle tracking models are introduced to describe particle movement under various flow conditions, i.e., the stochastic diffusion process, stochastic jump process, and stochastic jump diffusion process. While the stochastic diffusion process can be used to represent the stochastic movement of suspended particles in turbulent flows, the stochastic jump and the stochastic jump diffusion processes can be used to describe suspended particle movement in the occurrences of a sequence of extreme flows. An extreme flow herein is defined as a hydrologic flow event or a hydrodynamic flow phenomenon with a low probability of occurrence and a high impact on its ambient flow environment. In this paper, the suspended sediment particle is assumed to immediately follow the extreme flows in the jump process (i.e. the time lag between the flow particle and the sediment particle in extreme flows is considered negligible). In the proposed particle tracking models, a random term mainly caused by fluid eddy motions is modeled as a Wiener process, while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process. The frequency of occurrence of the extreme flows in the proposed particle tracking model can be explicitly accounted for by the Poisson process when evaluating particle movement. The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations. The ensemble mean and variance of particle velocity are verified with available data. Applicability of the proposed stochastic particle tracking models for sediment transport modeling is also discussed.
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.
Energy Technology Data Exchange (ETDEWEB)
Sinitsyn, Nikolai A [Los Alamos National Laboratory
2008-01-01
We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the noncyclic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We also discuss a model, where this correction qualitatively changes the outcome of reaction kinetics.
A stochastic evolutionary model generating a mixture of exponential distributions
Fenner, Trevor; Loizou, George
2015-01-01
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in \\cite{FENN15} so that it can generate mixture models,in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
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...
From cusps to cores: a stochastic model
El-Zant, Amr; Combes, Francoise
2016-01-01
The cold dark matter model of structure formation faces apparent problems on galactic scales. Several threads point to excessive halo concentration, including central densities that rise too steeply with decreasing radius. Yet, random fluctuations in the gaseous component can 'heat' the centres of haloes, decreasing their densities. We present a theoretical model deriving this effect from first principles: stochastic variations in the gas density are converted into potential fluctuations that act on the dark matter; the associated force correlation function is calculated and the corresponding stochastic equation solved. Assuming a power law spectrum of fluctuations with maximal and minimal cutoff scales, we derive the velocity dispersion imparted to the halo particles and the relevant relaxation time. We further perform numerical simulations, with fluctuations realised as a Gaussian random field, which confirm the formation of a core within a timescale comparable to that derived analytically. Non-radial colle...
Suprathreshold stochastic resonance in neural processing tuned by correlation
Durrant, Simon; Kang, Yanmei; Stocks, Nigel; Feng, Jianfeng
2011-07-01
Suprathreshold stochastic resonance (SSR) is examined in the context of integrate-and-fire neurons, with an emphasis on the role of correlation in the neuronal firing. We employed a model based on a network of spiking neurons which received synaptic inputs modeled by Poisson processes stimulated by a stepped input signal. The smoothed ensemble firing rate provided an output signal, and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons. It was found that an SSR effect was present in this context. We then examined a more biophysically plausible scenario where the noise was not controlled directly, but instead was tuned by the correlation between the inputs. The SSR effect remained present in this scenario with nonzero noise providing improved information transmission, and it was found that negative correlation between the inputs was optimal. Finally, an examination of SSR in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade-off between supratheshold and subthreshold components. We discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing.
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...... the footbridge and when describing the action of the pedestrians (such as for instance the number of load harmonics). Focus is on estimating vertical structural response to single person loading....
Stochastic similarities between hydroclimatic processes for variability characterization
Dimitriadis, Panayiotis; Markonis, Yannis; Iliopoulou, Theano; Gournari, Naya; Deligiannis, Ilias; Kastis, Paris; Nasika, Xristina; Lerias, Eleutherios; Moustakis, Yannis; Petsiou, Amalia; Sotiriadou, Alexia; Stefanidis, Eleutherios; Tyrogiannis, Vassilis; Feloni, Elisavet; Koutsoyiannis, Demetris
2016-04-01
The most important hydroclimatic processes such as temperature, dew point, wind, precipitation and river discharges are investigated for their stochastic behaviour on annual scale through several historical records. We investigate the stochastic similarities between them in terms of long-term persistence and we comment on their statistical variability giving emphasis on the last period. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.
Liu, Meng; Wang, Ke; Wu, Qiong
2011-09-01
Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.
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...
A stochastic model of human gait dynamics
Ashkenazy, Yosef; M. Hausdorff, Jeffrey; Ch. Ivanov, Plamen; Eugene Stanley, H.
2002-12-01
We present a stochastic model of gait rhythm dynamics, based on transitions between different “neural centers”, that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the transition (hopping) range, the model can describe alterations in gait dynamics from childhood to adulthood-including a decrease in the correlation and volatility exponents with maturation. The model also generates time series with multifractal spectra whose broadness depends only on this parameter. Moreover, we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum, suggesting the possibility of a change in multifractality with maturation.
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
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...
Rozhok, Andrii I; Salstrom, Jennifer L; DeGregori, James
2014-12-01
Age-dependent tissue decline and increased cancer incidence are widely accepted to be rate-limited by the accumulation of somatic mutations over time. Current models of carcinogenesis are dominated by the assumption that oncogenic mutations have defined advantageous fitness effects on recipient stem and progenitor cells, promoting and rate-limiting somatic evolution. However, this assumption is markedly discrepant with evolutionary theory, whereby fitness is a dynamic property of a phenotype imposed upon and widely modulated by environment. We computationally modeled dynamic microenvironment-dependent fitness alterations in hematopoietic stem cells (HSC) within the Sprengel-Liebig system known to govern evolution at the population level. Our model for the first time integrates real data on age-dependent dynamics of HSC division rates, pool size, and accumulation of genetic changes and demonstrates that somatic evolution is not rate-limited by the occurrence of mutations, but instead results from aged microenvironment-driven alterations in the selective/fitness value of previously accumulated genetic changes. Our results are also consistent with evolutionary models of aging and thus oppose both somatic mutation-centric paradigms of carcinogenesis and tissue functional decline. In total, we demonstrate that aging directly promotes HSC fitness decline and somatic evolution via non-cell-autonomous mechanisms.
On cross-currency models with stochastic volatility and correlated interest rates
Grzelak, L.A.; Oosterlee, C.W.
2010-01-01
We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of
On cross-currency models with stochastic volatility and correlated interest rates
Grzelak, L.A.; Oosterlee, C.W.
2010-01-01
We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull
Extremes of independent stochastic processes: a point process approach
Dombry, Clément
2011-01-01
For each $n\\geq 1$, let $ {X_{in}, \\quad i \\geq 1} $ be independent copies of a nonnegative continuous stochastic process $X_{n}=(X_n(t))_{t\\in T}$ indexed by a compact metric space $T$. We are interested in the process of partial maxima [\\tilde M_n(u,t) =\\max {X_{in}(t), 1 \\leq i\\leq [nu]},\\quad u\\geq 0,\\ t\\in T.] where the brackets $[\\,\\cdot\\,]$ denote the integer part. Under a regular variation condition on the sequence of processes $X_n$, we prove that the partial maxima process $\\tilde M_n$ weakly converges to a superextremal process $\\tilde M$ as $n\\to\\infty$. We use a point process approach based on the convergence of empirical measures. Properties of the limit process are investigated: we characterize its finite-dimensional distributions, prove that it satisfies an homogeneous Markov property, and show in some cases that it is max-stable and self-similar. Convergence of further order statistics is also considered. We illustrate our results on the class of log-normal processes in connection with some r...
Stochastic modelling of river morphodynamics
Van Vuren, B.G.
2005-01-01
Modern river management has to reconcile a number of functions, such as protection against floods and provision of safe and efficient navigation, floodplain agriculture, ecology and recreation. Knowledge on uncertainty in fluvial processes is important to make this possible, to design effective rive
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 Jump-Diffusion Model with Stochastic Volatility and Durations
DEFF Research Database (Denmark)
Wei, Wei; Pelletier, Denis
Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price...... jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We adopt a bivariate Ornstein-Ulenbeck process to model intraday volatility and conditional duration. We develop a MCMC algorithm for the inference on irregularly spaced multivariate processes with jumps....... The algorithm provides smoothed estimates of the latent variables such as spot volatility, conditional duration, jump times, and jump sizes. We apply this model to IBM data and find that volatility and conditional duration are interdependent. We also find that jumps play an important role in return variation...
Adaptive mesh refinement for stochastic reaction-diffusion processes
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2011-01-01
We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.
Modelling conjugation with stochastic differential equations.
Philipsen, K R; Christiansen, L E; Hasman, H; Madsen, H
2010-03-07
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 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 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 to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems.
Stochastic Modelling of Gompertzian Tumor Growth
O'Rourke, S. F. C.; Behera, A.
2009-08-01
We study the effect of correlated noise in the Gompertzian tumor growth model for non-zero correlation time. The steady state probability distributions and average population of tumor cells are analyzed within the Fokker-Planck formalism to investigate the importance of additive and multiplicative noise. We find that the correlation strength and correlation time have opposite effects on the steady state probability distributions. It is observed that the non-bistable Gompertzian model, driven by correlated noise exhibits a stochastic resonance and phase transition. This behaviour of the Gompertz model is unaffected with the change of correlation time and occurs as a result of multiplicative noise.
Stochastic Differential Equation-Based Flexible Software Reliability Growth Model
Directory of Open Access Journals (Sweden)
P. K. Kapur
2009-01-01
Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.
Stochastic Models of Polymer Systems
2016-01-01
field limit of a dynamical model for polymer systems, Science China Mathematics , (11 2012): 0. doi: TOTAL: 1 Number of Non Peer-Reviewed Conference...4.0 (4.0 max scale): Number of graduating undergraduates funded by a DoD funded Center of Excellence grant for Education , Research and Engineering...undergraduates funded by your agreement who graduated during this period and will receive scholarships or fellowships for further studies in science
Chang, Shuhua; Wang, Xinyu; Wang, Zheng
2015-01-01
Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion (GBM). We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman (HJB) equations sati...
Zhang, Yue; Zheng, Yan; Liu, Xi; Zhang, Qingling; Li, Aihua
2016-11-01
This study considers a class of differential algebraic stage-structured bio-economic models with stochastic fluctuations. The stochastic bio-economic model is simplified to an Itô equation using the stochastic averaging method. The stochastic stability, Hopf bifurcation, and P-bifurcation are discussed based on the singular boundary theory of the diffusion process for the system and the invariant measure theory of dynamic systems. Numerical simulations are presented to illustrate our main results.
Representing Turbulence Model Uncertainty with Stochastic PDEs
Oliver, Todd; Moser, Robert
2012-11-01
Validation of and uncertainty quantification for extrapolative predictions of RANS turbulence models are necessary to ensure that the models are not used outside of their domain of applicability and to properly inform decisions based on such predictions. In previous work, we have developed and calibrated statistical models for these purposes, but it has been found that incorporating all the knowledge of a domain expert--e.g., realizability, spatial smoothness, and known scalings--in such models is difficult. Here, we explore the use of stochastic PDEs for this purpose. The goal of this formulation is to pose the uncertainty model in a setting where it is easier for physical modelers to express what is known. To explore the approach, multiple stochastic models describing the error in the Reynolds stress are coupled with multiple deterministic turbulence models to make uncertain predictions of channel flow. These predictions are compared with DNS data to assess their credibility. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615].
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
. 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......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...... 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...
Stochastic Modeling and Analysis of Power System with Renewable Generation
DEFF Research Database (Denmark)
Chen, Peiyuan
to evaluate year-to-year variation of wind power generation through a sensitivity analysis and to forecast very short-term wind power through a model-based prediction method. The stochastic load model is established on the basis of a seasonal autoregressive moving average (ARMA) process. It is demonstrated...... 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...... that minimizes the expectation of power losses of a 69-bus distribution system by controlling the power factor of WTs. The optimization is subjected to the probabilistic constraints of bus voltage and line current. The algorithm combines a constrained nonlinear optimization algorithm and a Monte Carlo based PLF...
Stochastic calculus for fractional Brownian motion and related processes
Mishura, Yuliya S
2008-01-01
The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0
Arta process model of maritime clutter and targets
CSIR Research Space (South Africa)
McDonald
2012-10-01
Full Text Available A coherent autoregressive–to–anything (ARTA) stationary stochastic process for modelling maritime clutter and targets is presented in this paper. The ARTA stochastic process model is an improvement over previous models in the sense...
Universality Class in Abelian Sandpile Models with Stochastic Toppling Rules
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We present a stochastic critical slope sandpile model, where the amount of grains that fall in an overturning event is stochastic variable. The model is local, conservative, and Abelian. We apply the moment analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. Numerical results show that this model, Oslo model, and one-dimensional Abelian Manna model have the same critical behavior although the three models have different stochastic toppling rules, which provides evidences suggesting that Abelian sandpile models with different stochastic toppling rules are in the same universality class.
Stochastic modeling of triple-frequency BeiDou signals: estimation, assessment and impact analysis
Li, Bofeng
2016-07-01
Stochastic models are important in global navigation satellite systems (GNSS) estimation problems. One can achieve reliable ambiguity resolution and precise positioning only by use of a suitable stochastic model. The BeiDou system has received increased research focus, but based only on empirical stochastic models from the knowledge of GPS. In this paper, we will systematically study the estimation, assessment and impacts of a triple-frequency BeiDou stochastic model. In our estimation problem, a single-difference, geometry-free functional model is used to extract pure random noise. A very sophisticated structure of unknown variance matrix is designed to allow the estimation of satellite-specific variances, cross correlations between two arbitrary frequencies, as well as the time correlations for phase and code observations per frequency. In assessing the stochastic models, six data sets with four brands of BeiDou receivers on short and zero-length baselines are processed, and the results are compared. In impact analysis of stochastic model, the performance of integer ambiguity resolution and positioning are numerically demonstrated using a realistic stochastic model. The results from ultrashort (shorter than 10 m) and zero-length baselines indicate that BeiDou stochastic models are affected by both observation and receiver brands. The observation variances have been modeled by an elevation-dependent function, but the modeling errors for geostationary earth orbit (GEO) satellites are larger than for inclined geosynchronous satellite orbit (IGSO) and medium earth orbit (MEO) satellites. The stochastic model is governed by both the internal errors of the receiver and external errors at the site. Different receivers have different capabilities for resisting external errors. A realistic stochastic model is very important for achieving ambiguity resolution with a high success rate and small false alarm and for determining realistic variances for position estimates. To
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...
Stochastic MPC with applications to process control
Jurado, I.; Millán, P.; Quevedo, D.; Rubio, F. R.
2015-04-01
This paper presents a model predictive control formulation for Networked Control Systems subject to independent and identically distributed delays and packet dropouts. The design takes into account the presence of a communication network in the control loop, resorting to a buffer at the actuator side to store and consistently apply delayed control sequences when fresh control inputs are not available. The proposed approach uses a statistical description of transmissions to optimise the expected future control performance conditioned upon the current system state, previously calculated control packets and transmission acknowledgements. Experimental studies using a quadruple tank process illustrate the applicability of the method to process control.
Stochastic Downscaling of Digital Elevation Models
Rasera, Luiz Gustavo; Mariethoz, Gregoire; Lane, Stuart N.
2016-04-01
High-resolution digital elevation models (HR-DEMs) are extremely important for the understanding of small-scale geomorphic processes in Alpine environments. In the last decade, remote sensing techniques have experienced a major technological evolution, enabling fast and precise acquisition of HR-DEMs. However, sensors designed to measure elevation data still feature different spatial resolution and coverage capabilities. Terrestrial altimetry allows the acquisition of HR-DEMs with centimeter to millimeter-level precision, but only within small spatial extents and often with dead ground problems. Conversely, satellite radiometric sensors are able to gather elevation measurements over large areas but with limited spatial resolution. In the present study, we propose an algorithm to downscale low-resolution satellite-based DEMs using topographic patterns extracted from HR-DEMs derived for example from ground-based and airborne altimetry. The method consists of a multiple-point geostatistical simulation technique able to generate high-resolution elevation data from low-resolution digital elevation models (LR-DEMs). Initially, two collocated DEMs with different spatial resolutions serve as an input to construct a database of topographic patterns, which is also used to infer the statistical relationships between the two scales. High-resolution elevation patterns are then retrieved from the database to downscale a LR-DEM through a stochastic simulation process. The output of the simulations are multiple equally probable DEMs with higher spatial resolution that also depict the large-scale geomorphic structures present in the original LR-DEM. As these multiple models reflect the uncertainty related to the downscaling, they can be employed to quantify the uncertainty of phenomena that are dependent on fine topography, such as catchment hydrological processes. The proposed methodology is illustrated for a case study in the Swiss Alps. A swissALTI3D HR-DEM (with 5 m resolution
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
Directory of Open Access Journals (Sweden)
J. Lévy Véhel
2013-09-01
Full Text Available Multifractional Brownian motion (mBm has proved to be a useful tool in various areas of geophysical modelling. Although a versatile model, mBm is of course not always an adequate one. We present in this work several other stochastic processes which could potentially be useful in geophysics. The first alternative type is that of self-regulating processes: these are models where the local regularity is a function of the amplitude, in contrast to mBm where it is tuned exogenously. We demonstrate the relevance of such models for digital elevation maps and for temperature records. We also briefly describe two other types of alternative processes, which are the counterparts of mBm and of self-regulating processes when the intensity of local jumps is considered in lieu of local regularity: multistable processes allow one to prescribe the local intensity of jumps in space/time, while this intensity is governed by the amplitude for self-stabilizing processes.
A Specification Test of Stochastic Diffusion Models
Institute of Scientific and Technical Information of China (English)
Shu-lin ZHANG; Zheng-hong WEI; Qiu-xiang BI
2013-01-01
In this paper,we propose a hypothesis testing approach to checking model mis-specification in continuous-time stochastic diffusion model.The key idea behind the development of our test statistic is rooted in the generalized information equality in the context of martingale estimating equations.We propose a bootstrap resampling method to implement numerically the proposed diagnostic procedure.Through intensive simulation studies,we show that our approach is well performed in the aspects of type Ⅰ error control,power improvement as well as computational efficiency.
Stochastic Gompertz model of tumour cell growth.
Lo, C F
2007-09-21
In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.
Stochastic Optimal Control Models for Online Stores
Bradonjić, Milan
2011-01-01
We present a model for the optimal design of an online auction/store by a seller. The framework we use is a stochastic optimal control problem. In our setting, the seller wishes to maximize her average wealth level, where she can control her price per unit via her reputation level. The corresponding Hamilton-Jacobi-Bellmann equation is analyzed for an introductory case. We then turn to an empirically justified model, and present introductory analysis. In both cases, {\\em pulsing} advertising strategies are recovered for resource allocation. Further numerical and functional analysis will appear shortly.
Realistic boundary conditions for stochastic simulations of reaction-diffusion processes
Erban, R; Erban, Radek
2006-01-01
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed and precise picture, and several stochastic simulation algorithms have been proposed in recent years. Such models typically give the same description of the reaction-diffusion processes far from the boundary of the simulated domain, but the behaviour close to a reactive boundary (e.g. a membrane with receptors) is unfortunately model-dependent. In this paper, we study four different approaches to stochastic modelling of reaction-diffusion problems and show the correct choice of the boundary condition for each model. The reactive boundary is treated as partially reflective, which means that some molecules hitting the boundary are adsorbed (e.g. bound to the receptor) and some molecul...
Stochastic modeling of deterioration in nuclear power plant components
Yuan, Xianxun
2007-12-01
The risk-based life-cycle management of engineering systems in a nuclear power plant is intended to ensure safe and economically efficient operation of energy generation infrastructure over its entire service life. An important element of life-cycle management is to understand, model and forecast the effect of various degradation mechanisms affecting the performance of engineering systems, structures and components. The modeling of degradation in nuclear plant components is confounded by large sampling and temporal uncertainties. The reason is that nuclear systems are not readily accessible for inspections due to high level of radiation and large costs associated with remote data collection methods. The models of degradation used by industry are largely derived from ordinary linear regression methods. The main objective of this thesis is to develop more advanced techniques based on stochastic process theory to model deterioration in engineering components with the purpose of providing more scientific basis to life-cycle management of aging nuclear power plants. This thesis proposes a stochastic gamma process (GP) model for deterioration and develops a suite of statistical techniques for calibrating the model parameters. The gamma process is a versatile and mathematically tractable stochastic model for a wide variety of degradation phenomena, and another desirable property is its nonnegative, monotonically increasing sample paths. In the thesis, the GP model is extended by including additional covariates and also modeling for random effects. The optimization of age-based replacement and condition-based maintenance strategies is also presented. The thesis also investigates improved regression techniques for modeling deterioration. A linear mixed-effects (LME) regression model is presented to resolve an inconsistency of the traditional regression models. The proposed LME model assumes that the randomness in deterioration is decomposed into two parts: the unobserved
COMPUTER DATA ANALYSIS AND MODELING: COMPLEX STOCHASTIC DATA AND SYSTEMS
2010-01-01
This collection of papers includes proceedings of the Ninth International Conference “Computer Data Analysis and Modeling: Complex Stochastic Data and Systems” organized by the Belarusian State University and held in September 2010 in Minsk. The papers are devoted to the topical problems: robust and nonparametric data analysis; statistical analysis of time series and forecasting; multivariate data analysis; design of experiments; statistical signal and image processing...
Nonlinear stochastic modeling of river dissolved-oxygen
Energy Technology Data Exchange (ETDEWEB)
Tabios, G.Q. III.
1984-01-01
An important aspect of water quality modeling is forecasting water quality variables for real-time management and control applications to enhance, maintain and sustain desirable water qualities. The major objective of this research is to develop daily time series models for forecasting river dissolved-oxygen (DO). The modeling approach adopted herein combines deterministic and stochastic concepts for determining properties of the DO process based on time series data and dynamic mechanisms governing the said process. This is accomplished by deriving a general DO stochastic model structure based on a modified Streeter-Phelps DO-BOD dynamic model. Then some types of nonlinear models namely, self-exciting threshold autoregressive-moving average (SETARMA), amplitude-dependent autoregressive (ADAR) and bilinear (BL) models, and the class of linear autoregressive-moving average (ARMA) models are adopted for model identification and parameter estimation. Six stream-water quality gaging stations located in the eastern portion of the continental U.S.A. are utilized in this study. Various orders of ARMA, SETARMA, ADAR and BL models are fitted to the data. Results obtained indicated that ADAR and BL models are superior for one-step ahead forecasts, while SETARMA models are better for forecasts of longer lead times. In general, the SETARMA, ADAR and BL models show promise as alternative models for river DO time series modeling and forecasting with unique advantages in each.
Stochastic State Space Modelling of Nonlinear systems - With application to Marine Ecosystems
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg
to conflict with the concept of mass balances. One of the central conclusions of the thesis is that the stochastic formulations should be an integral part of the model formulation. As discrete-time stochastic processes are simpler to handle numerically than continuous-time stochastic processes, I start......This thesis deals with stochastic dynamical systems in discrete and continuous time. Traditionally dynamical systems in continuous time are modelled using Ordinary Differential Equations (ODEs). Even the most complex system of ODEs will not be able to capture every detail of a complex system like...... a natural ecosystem, and hence residual variation between the model and observations will always remain. In stochastic state-space models the residual variation is separated into observation and system noise and a main theme of the thesis is a proper description of the system noise. Additive Gaussian noise...
Mjelde, James W.; Harris, Wesley D.; Conner, J. Richard; Schnitkey, Gary D.; Glover, Michael K.; Garoian, Lee
1992-01-01
Concepts associated with stochastic process containing multiple transition matricies are discussed. It is proved that under certain conditions, a process with m transition matrices has m unique limiting probability vectors. This result extends the notion of discrete Markov processes to problems with intrayear and interyear dynamics. An example using a large DP model illustrates the usefulness of the concepts developed to applied problems.
Stochastic simulation of spatially correlated geo-processes
Christakos, G.
1987-01-01
In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simu??lation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail. ?? 1987 International Association for Mathematical Geology.
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...... that describes the variation between subjects. The ODE setup implies that the variation for a single subject is described by a single parameter (or vector), namely the variance (covariance) of the residuals. Furthermore the prediction of the states is given as the solution to the ODEs and hence assumed...... 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...
? filtering for stochastic systems driven by Poisson processes
Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya
2015-01-01
This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.
Estimating Stochastic Volatility Models using Prediction-based Estimating Functions
DEFF Research Database (Denmark)
Lunde, Asger; Brix, Anne Floor
In this paper prediction-based estimating functions (PBEFs), introduced in Sørensen (2000), are reviewed and PBEFs for the Heston (1993) stochastic volatility model are derived. The finite sample performance of the PBEF based estimator is investigated in a Monte Carlo study, and compared to the p......In this paper prediction-based estimating functions (PBEFs), introduced in Sørensen (2000), are reviewed and PBEFs for the Heston (1993) stochastic volatility model are derived. The finite sample performance of the PBEF based estimator is investigated in a Monte Carlo study, and compared...... to the performance of the GMM estimator based on conditional moments of integrated volatility from Bollerslev and Zhou (2002). The case where the observed log-price process is contaminated by i.i.d. market microstructure (MMS) noise is also investigated. First, the impact of MMS noise on the parameter estimates from...
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.
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
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.
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
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 ...
Anomalous scaling of stochastic processes and the Moses effect
Chen, Lijian; Bassler, Kevin E.; McCauley, Joseph L.; Gunaratne, Gemunu H.
2017-04-01
The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t1/2. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.
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...
Optimization Framework for Stochastic Modeling of Annual Streamflows
Srivastav, R. K.; Srinivasan, K.; Sudheer, K.
2008-12-01
Synthetic streamflow data generation involves the synthesis of likely streamflow patterns that are statistically indistinguishable from the observed streamflow data. The various kinds of stochastic models adopted for streamflow generation in hydrology are: i) parametric models which hypothesize the form of the dependence structure and the distributional form a priori (examples are AR, ARMA); ii) Nonparametric models (examples are bootstrap/kernel based methods), which characterize the laws of chance, describing the stream flow process, without recourse to prior assumptions as to the form or structure of these laws; iii) Hybrid models which blend both parametric and non-parametric models advantageously to model the streamflows effectively. Despite many of these developments that have taken place in the field of stochastic modeling of streamflows over the last four decades, accurate prediction of the storage and the critical drought (water use) characteristics has been posing a persistent challenge to the stochastic modeler. This may be because, usually, the stochastic streamflow model parameters are estimated by minimizing a statistically based objective function (such as maximum likelihood (MLE) or least squares estimation) and subsequently the efficacy of the models is being validated based on the accuracy of prediction of the estimates of the water- use characteristics. In this study a framework is proposed to find the optimal hybrid model (blend of ARMA(1,1) and moving block bootstrap (MBB)) based on the explicit objective function of minimizing the relative bias in estimating the storage capacity of the reservoir. The optimal parameter set of the hybrid model is obtained based on the search over a multi-dimensional parameter space involving simultaneous exploration of the parametric (ARMA[1,1]) as well as the non-parametric (MBB) components. This is achieved using the efficient evolutionary search based optimization tool namely, non-dominated sorting genetic
Extending Newtonian Dynamics to Include Stochastic Processes
Zak, Michail
2009-01-01
A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.
Stochastic models of solute transport in highly heterogeneous geologic media
Energy Technology Data Exchange (ETDEWEB)
Semenov, V.N.; Korotkin, I.A.; Pruess, K.; Goloviznin, V.M.; Sorokovikova, O.S.
2009-09-15
A stochastic model of anomalous diffusion was developed in which transport occurs by random motion of Brownian particles, described by distribution functions of random displacements with heavy (power-law) tails. One variant of an effective algorithm for random function generation with a power-law asymptotic and arbitrary factor of asymmetry is proposed that is based on the Gnedenko-Levy limit theorem and makes it possible to reproduce all known Levy {alpha}-stable fractal processes. A two-dimensional stochastic random walk algorithm has been developed that approximates anomalous diffusion with streamline-dependent and space-dependent parameters. The motivation for introducing such a type of dispersion model is the observed fact that tracers in natural aquifers spread at different super-Fickian rates in different directions. For this and other important cases, stochastic random walk models are the only known way to solve the so-called multiscaling fractional order diffusion equation with space-dependent parameters. Some comparisons of model results and field experiments are presented.
Stochastic Modeling of Non-equilibrium Bedload Transport
Kuai, Z.; Tsai, C. W.
2009-05-01
Traditional stochastic bed load models aimed to solve for the equilibrium bedload transport rate by matching the rate of bed erosion with the rate of deposition. Bedload transport can be in nonequilibrium even under the steady flow condition, as the quantity of moving particles in the bedload layer may vary. In a nonequilibrium condition, the interchange of sediment particles occurs not only between the bedload layer and the bed surface, but also across the interface between bedload and suspended load. The proposed approach attempts to add a new bedload-suspended load interchange layer to a stochastic bedlod transport model based on the Markov chain. The bedload transport rate is the product of the total particle volume in saltation and the average saltating velocity. We can quantify the number of saltating particles by modeling the occupancy probabilities vector of particles staying in three states (i.e., bed surface, bedload layer, and the interchange layer between the bedload and the suspended load.). The new stochastic bedload relation is validated against existing bedload model. The sudden change of flow and/or sediment condition leads to changes in the transition probabilities. The influence of sudden changes in flow-sediment properties on the bedload transport rate is investigated in this preliminary study. It is found that the neglecting the exchange process between the bedload layer and the suspended layer may lead to non-negligible errors in bedload calculation when the flow and/or sediment conditions change.
Stochastic delay models for molecular clocks and somite formation
Burrage, Kevin; Burrage, Pamela; Leier, André; Marquez-Lago, Tatiana T.
2007-12-01
Delays are an important feature in temporal models of genetic regulation due to slow biochemical processes such as transcription and translation. In this paper we show how to model intrinsic noise effects in a delayed setting by either using a delay stochastic simulation algorithm (DSSA) or, for larger and more complex systems, a generalized Binomial tau-leap method (Bt-DSSA). As a particular application we apply these ideas to modeling somite segmentation in zebrafish across a number of cells in which two linked oscillatory genes her1 and her7 are synchronized via Notch signaling between the cells.
Stochastic effects in a seasonally forced epidemic model
Rozhnova, G.; Nunes, A.
2010-10-01
The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.
Stochastic effects in a seasonally forced epidemic model
Rozhnova, Ganna
2010-01-01
The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.
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
Directory of Open Access Journals (Sweden)
Kyung-Min Chung
Full Text Available Despite years of research, the reprogramming of human somatic cells to pluripotency remains a slow, inefficient process, and a detailed mechanistic understanding of reprogramming remains elusive. Current models suggest reprogramming to pluripotency occurs in two-phases: a prolonged stochastic phase followed by a rapid deterministic phase. In this paradigm, the early stochastic phase is marked by the random and gradual expression of pluripotency genes and is thought to be a major rate-limiting step in the successful generation of induced Pluripotent Stem Cells (iPSCs. Recent evidence suggests that the epigenetic landscape of the somatic cell is gradually reset during a period known as the stochastic phase, but it is known neither how this occurs nor what rate-limiting steps control progress through the stochastic phase. A precise understanding of gene expression dynamics in the stochastic phase is required in order to answer these questions. Moreover, a precise model of this complex process will enable the measurement and mechanistic dissection of treatments that enhance the rate or efficiency of reprogramming to pluripotency. Here we use single-cell transcript profiling, FACS and mathematical modeling to show that the stochastic phase is an ordered probabilistic process with independent gene-specific dynamics. We also show that partially reprogrammed cells infected with OSKM follow two trajectories: a productive trajectory toward increasingly ESC-like expression profiles or an alternative trajectory leading away from both the fibroblast and ESC state. These two pathways are distinguished by the coordinated expression of a small group of chromatin modifiers in the productive trajectory, supporting the notion that chromatin remodeling is essential for successful reprogramming. These are the first results to show that the stochastic phase of reprogramming in human fibroblasts is an ordered, probabilistic process with gene-specific dynamics and to
Chung, Kyung-Min; Kolling, Frederick W; Gajdosik, Matthew D; Burger, Steven; Russell, Alexander C; Nelson, Craig E
2014-01-01
Despite years of research, the reprogramming of human somatic cells to pluripotency remains a slow, inefficient process, and a detailed mechanistic understanding of reprogramming remains elusive. Current models suggest reprogramming to pluripotency occurs in two-phases: a prolonged stochastic phase followed by a rapid deterministic phase. In this paradigm, the early stochastic phase is marked by the random and gradual expression of pluripotency genes and is thought to be a major rate-limiting step in the successful generation of induced Pluripotent Stem Cells (iPSCs). Recent evidence suggests that the epigenetic landscape of the somatic cell is gradually reset during a period known as the stochastic phase, but it is known neither how this occurs nor what rate-limiting steps control progress through the stochastic phase. A precise understanding of gene expression dynamics in the stochastic phase is required in order to answer these questions. Moreover, a precise model of this complex process will enable the measurement and mechanistic dissection of treatments that enhance the rate or efficiency of reprogramming to pluripotency. Here we use single-cell transcript profiling, FACS and mathematical modeling to show that the stochastic phase is an ordered probabilistic process with independent gene-specific dynamics. We also show that partially reprogrammed cells infected with OSKM follow two trajectories: a productive trajectory toward increasingly ESC-like expression profiles or an alternative trajectory leading away from both the fibroblast and ESC state. These two pathways are distinguished by the coordinated expression of a small group of chromatin modifiers in the productive trajectory, supporting the notion that chromatin remodeling is essential for successful reprogramming. These are the first results to show that the stochastic phase of reprogramming in human fibroblasts is an ordered, probabilistic process with gene-specific dynamics and to provide a precise
Stochastic spatio-temporal modelling with PCRaster Python
Karssenberg, D.; Schmitz, O.; de Jong, K.
2012-04-01
PCRaster Python is a software framework for building spatio-temporal models of land surface processes (Karssenberg, Schmitz, Salamon, De Jong, & Bierkens, 2010; PCRaster, 2012). Building blocks of models are spatial operations on raster maps, including a large suite of operations for water and sediment routing. These operations, developed in C++, are available to model builders as Python functions. Users create models by combining these functions in a Python script. As construction of large iterative models is often difficult and time consuming for non-specialists in programming, the software comes with a set of Python framework classes that provide control flow for static modelling, temporal modelling, stochastic modelling using Monte Carlo simulation, and data assimilation techniques including the Ensemble Kalman filter and the Particle Filter. A framework for integrating model components with different time steps and spatial discretization is currently available as a prototype (Schmitz, de Jong, & Karssenberg, in review). The software includes routines for visualisation of stochastic spatio-temporal data for prompt, interactive, visualisation of model inputs and outputs. Visualisation techniques include animated maps, time series, probability distributions, and animated maps with exceedance probabilities. The PCRaster Python software is used by researchers from a large range of disciplines, including hydrology, ecology, sedimentology, and land use change studies. Applications include global scale hydrological modelling and error propagation in large-scale land use change models. The software runs on MS Windows and Linux operating systems, and OS X (under development).
Evaluation of Uncertainty in Runoff Analysis Incorporating Theory of Stochastic Process
Yoshimi, Kazuhiro; Wang, Chao-Wen; Yamada, Tadashi
2015-04-01
The aim of this paper is to provide a theoretical framework of uncertainty estimate on rainfall-runoff analysis based on theory of stochastic process. SDE (stochastic differential equation) based on this theory has been widely used in the field of mathematical finance due to predict stock price movement. Meanwhile, some researchers in the field of civil engineering have investigated by using this knowledge about SDE (stochastic differential equation) (e.g. Kurino et.al, 1999; Higashino and Kanda, 2001). However, there have been no studies about evaluation of uncertainty in runoff phenomenon based on comparisons between SDE (stochastic differential equation) and Fokker-Planck equation. The Fokker-Planck equation is a partial differential equation that describes the temporal variation of PDF (probability density function), and there is evidence to suggest that SDEs and Fokker-Planck equations are equivalent mathematically. In this paper, therefore, the uncertainty of discharge on the uncertainty of rainfall is explained theoretically and mathematically by introduction of theory of stochastic process. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation) due to describe it as difference formula, because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. This is attributed to the observed rainfall by rain-gauge station and radar rain-gauge system. As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE (stochastic differential equation) and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be
Stochastic modelling and analysis of IMU sensor errors
Zaho, Y.; Horemuz, M.; Sjöberg, L. E.
2011-12-01
The performance of a GPS/INS integration system is greatly determined by the ability of stand-alone INS system to determine position and attitude within GPS outage. The positional and attitude precision degrades rapidly during GPS outage due to INS sensor errors. With advantages of low price and volume, the Micro Electrical Mechanical Sensors (MEMS) have been wildly used in GPS/INS integration. Moreover, standalone MEMS can keep a reasonable positional precision only a few seconds due to systematic and random sensor errors. General stochastic error sources existing in inertial sensors can be modelled as (IEEE STD 647, 2006) Quantization Noise, Random Walk, Bias Instability, Rate Random Walk and Rate Ramp. Here we apply different methods to analyze the stochastic sensor errors, i.e. autoregressive modelling, Gauss-Markov process, Power Spectral Density and Allan Variance. Then the tests on a MEMS based inertial measurement unit were carried out with these methods. The results show that different methods give similar estimates of stochastic error model parameters. These values can be used further in the Kalman filter for better navigation accuracy and in the Doppler frequency estimate for faster acquisition after GPS signal outage.
Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes
Abrams, D.; Williams, C.
1999-01-01
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.
Conditional Stochastic Processes Applied to Wave Load Predictions
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
2015-01-01
The concept of conditional stochastic processes provides a powerful tool for evaluation and estimation of wave loads on ships and offshore structures. This article first considers conditional waves with a focus on critical wave episodes. Then the inherent uncertainty in the results is illustrated...
Counting statistics of non-markovian quantum stochastic processes
DEFF Research Database (Denmark)
Flindt, Christian; Novotny, T.; Braggio, A.
2008-01-01
We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of t...
Stochastic process switching when the time is ripe
Veestraeten, D.
2011-01-01
Stochastic process switching typically links one mode (absorption or reflection) with one choice on timing (state- or time-contingent). Sutherland (1995) combined absorption with both choices on timing allowing the switch to take place at first hitting or at a given point of time, whichever date com
Systematic parameter inference in stochastic mesoscopic modeling
Lei, Huan; Li, Zhen; Karniadakis, George
2016-01-01
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....
Optimal information diffusion in stochastic block models
Curato, Gianbiagio
2016-01-01
We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two community structure where the initial set of informed nodes lies only in one of the two communities and we look for optimal network structures, i.e. those maximizing the asymptotic extent of the diffusion. We find that, constraining the mean degree and the fraction of initially informed nodes, the optimal structure can be assortative (modular), core-periphery, or even disassortative. We then look for minimal cost structures, i.e. those such that a minimal fraction of initially informed nodes is needed to trigger a global cascade. We find that the optimal networks are assortative but with a structure very close to a core-periphery graph, i.e. a very dense community linked to a much more sparsely connected periphery.
Sensitivity Study of Stochastic Walking Load Models
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2010-01-01
On flexible structures such as footbridges and long-span floors, walking loads may generate excessive structural vibrations and serviceability problems. The problem is increasing because of the growing tendency to employ long spans in structural design. In many design codes, the vibration...... serviceability limit state is assessed using a walking load model in which the walking parameters are modelled deterministically. However, the walking parameters are stochastic (for instance the weight of the pedestrian is not likely to be the same for every footbridge crossing), and a natural way forward...... investigates whether statistical distributions of bridge response are sensitive to some of the decisions made by the engineer doing the analyses. For the paper a selected part of potential influences are examined and footbridge responses are extracted using Monte-Carlo simulations and focus is on estimating...
Zacharuk, Matthias; Stamen, Dolaptchiev; Ulrich, Achatz; Ilya, Timofeyev
2016-04-01
Due to the finite spatial resolution in numerical atmospheric models subgrid-scale (SGS) processes are excluded. A SGS parameterization of these excluded processes might improve the model on all scales. To parameterize the SGS processes we choose the MTV stochastic mode reduction (Majda, Timofeyev, Vanden-Eijnden 2001, A mathematical framework for stochastic climate models. Commun. Pure Appl. Math., 54:891-974). For this the model is separated into fast and slow processes. Using the statistics of the fast processes, a SGS parameterization is found. To identify fast processes the state vector of the model is separated into two state vectors. One vector is the average of the full model state vector in a coarse grid cell. The other describes SGS processes which are defined as the deviation of the full state vector from the coarse cell average. If the SGS vector decorrelates faster in time than the coarse grid vector, the interactions of SGS processes in the equation of the SGS processes are replaced by a local Ornstein-Uhlenbeck process. Afterwards the MTV SGS parameterization can be derived. This method was successfully applied on the Burgers-equation (Dolaptchiev et al. 2013, Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation. Theor. Comp. Fluid Dyn., 27:297-317). In this study we consider a more atmosphere like model and choose a model of the one dimensional shallow water equations (SWe). It will be shown, that the fine state vector decorrelates faster than the coarse state vector. Due to the non-polynomial form of the SWe in flux formulation an approximation of all 1/h (h = fluid depth) terms needs to be done, except of the interactions between coarse state vector to coarse state vector. It will be shown, that this approximation has only minor impact on the model results. In the following the model with the local Ornstein-Uhlenbeck process approximation of SGS interactions is analyzed and compared to the
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...
Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation
2015-01-01
This study proposes a novel data-based approach for estimating the parameters of a stochastic hybrid model describing the traffic flow in an urban traffic network with signalized intersections. The model represents the evolution of the traffic flow rate, measuring the number of vehicles passing a given location per time unit. This traffic flow rate is described using a mode-dependent first-order autoregressive (AR) stochastic process. The parameters of the AR process take different values dep...
Cultural evolution as a nonstationary stochastic process
DEFF Research Database (Denmark)
Nicholson, Arwen; Sibani, Paolo
2016-01-01
We present an individual based model of cultural evolution, where interacting agents are coded by binary strings standing for strategies for action, blueprints for products or attitudes and beliefs. The model is patterned on an established model of biological evolution, the Tangled Nature Model (...... qualitatively reproduce the flurry of cultural activity which follows a disruptive innovation....
Viscosity methods for multiscale financial models with stochastic volatility
Bardi, Martino; Cesaroni, Annalisa; Ghilli, Daria; Scotti, Andrea
2014-01-01
Parallel session; International audience; Introduction on models Financial models and stochastic volatility, Gaussian or with jumps Fast stochastic volatility Part 1 Control systems with random parameters and multiple scales The Hamilton-Jacobi-Bellman approach to Singular Perturbations I Tools I Assumptions I A convergence result Applications to finance Part 2 Large deviations for small time to maturity: see also Daria Ghilli's poster tomorrow
High order discretization schemes for stochastic volatility models
Jourdain, Benjamin
2009-01-01
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using It\\^o's formula, we get rid, in the asset price dynamics, of the stochastic integral with respect to the Brownian motion driving this SDE. Taking advantage of this structure, we propose - a scheme, based on the Milstein discretization of this SDE, with order one of weak trajectorial convergence for the asset price, - a scheme, based on the Ninomiya-Victoir discretization of this SDE, with order two of weak convergence for the asset price. We also propose a specific scheme with improved convergence properties when the volatility of the asset price is driven by an Orstein-Uhlenbeck process. We confirm the theoretical rates of convergence by numerical experiments and show that our schemes are well adapted to the multilevel Monte Carlo method introduced by Giles [2008a,b].
A Stochastic Unit Commitment Model for a Local CHP Plant
DEFF Research Database (Denmark)
Ravn, Hans V.; Riisom, Jannik; Schaumburg-Müller, Camilla
2005-01-01
Local CHP development in Denmark has during the 90’s been characterised by large growth primarily due to government subsidies in the form of feed-in tariffs. In line with the liberalisation process in the EU, Danish local CHPs of a certain size must operate on market terms from 2005. This paper...... presents a stochastic unit commitment model for a single local CHP plant (consisting of CHP unit, boiler, and heat storage facility) which takes into account varying spot prices. Further, additional technology is implemented in the model in the form of an immersion heater. Simulations are conducted using...
Stochastic Models of Defects in Wind Turbine Drivetrain Components
DEFF Research Database (Denmark)
Rafsanjani, Hesam Mirzaei; Sørensen, John Dalsgaard
2013-01-01
of the drivetrain will lead to substantial economic losses such as cost of lost energy production, cost of repairs, cost of crew and cost of transportation. For offshore wind turbines, the marine environment affects the repair & maintenance process and in some case because of the rush environment, the maintenance...... team cannot operate properly and the wind turbine does not work for several days and consequently the cost of lost energy increases drastically. In this paper is presented stochastic models for fatigue failure based on test data and the accuracy of the models are compared....
A Stochastic Model of RNA Translation with Frameshifting
Bailey, Brenae
2011-10-01
Many viruses can produce different proteins from the same RNA sequence by encoding them in overlapping genes. One mechanism that causes the ribosomes of infected cells to decode both genes is called programmed ribosomal frameshifting (PRF). Although PRF has been recognized for 25 years, the mechanism is not well understood. We have developed a model that treats RNA translation as a stochastic process in which the transition probabilities are based on the free energies of local molecular interactions. The model reproduces observed translation rates and frameshift efficiencies, and can be used to predict the effects of mutations in the viral RNA sequence on both the mean translation rate and the frameshift efficiency.
Stochastic modeling of reinforced concrete structures exposed to chloride attack
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Frier, Christian
2004-01-01
the reinforcement exceeds a critical threshold value. In the present paper a stochastic model is described by which the chloride content in a reinforced concrete structure can be estimated. The chloride ingress is modeled by a 2-dimensional diffusion process and the diffusion coefficient, surface chloride......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...
Detecting Character Dependencies in Stochastic Models of Evolution.
Chakrabarty, Deeparnab; Kannan, Sampath; Tian, Kevin
2016-03-01
Stochastic models of biological evolution generally assume that different characters (runs of the stochastic process) are independent and identically distributed. In this article we determine the asymptotic complexity of detecting dependence for some fairly general models of evolution, but simple models of dependence. A key difference from much of the previous work is that our algorithms work without knowledge of the tree topology. Specifically, we consider various stochastic models of evolution ranging from the common ones used by biologists (such as Cavender-Farris-Neyman and Jukes-Cantor models) to very general ones where evolution of different characters can be governed by different transition matrices on each edge of the evolutionary tree (phylogeny). We also consider several models of dependence between two characters. In the most specific model, on each edge of the phylogeny the joint distribution of the dependent characters undergoes a perturbation of a fixed magnitude, in a fixed direction from what it would be if the characters were evolving independently. More general dependence models don't require such a strong "signal." Instead they only require that on each edge, the perturbation of the joint distribution has a significant component in a specific direction. Our main results are nearly tight bounds on the induced or operator norm of the transition matrices that would allow us to detect dependence efficiently for most models of evolution and dependence that we consider. We make essential use of a new concentration result for multistate random variables of a Markov random field on arbitrary trivalent trees: We show that the random variable counting the number of leaves in any particular state has variance that is subquadratic in the number of leaves.
Improved dimensionally-reduced visual cortical network using stochastic noise modeling.
Tao, Louis; Praissman, Jeremy; Sornborger, Andrew T
2012-04-01
In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
2013-05-13
Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modelling approaches related to time subordination are considered and unified in the framework of self-similar stochastic processes. By assuming a single-particle fractional Brownian motion and that the two-particle correlation function decreases in time with a power law, the particle relative separation density is computed for the cases with time sub-ordination directed by a unilateral M-Wright density and by an extremal Lévy stable density. Looking for advisable mathematical properties (for instance, the stationarity of the increments), the corresponding self-similar stochastic processes are represented in terms of fractional Brownian motions with stochastic variance, whose profile is modelled by using the M-Wright density or the Lévy stable density.
Using Stochastic Model Checking to Provision Complex Business Services
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2012-01-01
bounds on resources consumed during execution of business processes. Accurate resource provisioning is often central to ensuring the safe execution of a process. We first introduce a formalised core subset of the Business Process Modelling and Notation (BPMN), which we extend with probabilistic and non......We present a framework for modelling and analysis of real-world business workflows. Business processes regularly form the basis for the design of software services, and frequently display complex stochastic behaviour. The accurate evaluation of their qualitative aspects can allow for determining...... of business processes including transient probabilities, timing, occurrence and ordering of events, and best- and worst-case scenarios. The developments presented are illustrated using an example from the health-care industry....
Fractional L\\'{e}vy-driven Ornstein--Uhlenbeck processes and stochastic differential equations
Fink, Holger; 10.3150/10-BEJ281
2011-01-01
Using Riemann-Stieltjes methods for integrators of bounded $p$-variation we define a pathwise integral driven by a fractional L\\'{e}vy process (FLP). To explicitly solve general fractional stochastic differential equations (SDEs) we introduce an Ornstein-Uhlenbeck model by a stochastic integral representation, where the driving stochastic process is an FLP. To achieve the convergence of improper integrals, the long-time behavior of FLPs is derived. This is sufficient to define the fractional L\\'{e}vy-Ornstein-Uhlenbeck process (FLOUP) pathwise as an improper Riemann-Stieltjes integral. We show further that the FLOUP is the unique stationary solution of the corresponding Langevin equation. Furthermore, we calculate the autocovariance function and prove that its increments exhibit long-range dependence. Exploiting the Langevin equation, we consider SDEs driven by FLPs of bounded $p$-variation for $p<2$ and construct solutions using the corresponding FLOUP. Finally, we consider examples of such SDEs, includin...
A Survey of Stochastic Simulation and Optimization Methods in Signal Processing
Pereyra, Marcelo; Schniter, Philip; Chouzenoux, Emilie; Pesquet, Jean-Christophe; Tourneret, Jean-Yves; Hero, Alfred O.; McLaughlin, Steve
2016-03-01
Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inference in models that are analytically intractable and beyond the scope of deterministic inference methods. They have been recently successfully applied to many difficult problems involving complex statistical models and sophisticated (often Bayesian) statistical inference techniques. This survey paper offers an introduction to stochastic simulation and optimization methods in signal and image processing. The paper addresses a variety of high-dimensional Markov chain Monte Carlo (MCMC) methods as well as deterministic surrogate methods, such as variational Bayes, the Bethe approach, belief and expectation propagation and approximate message passing algorithms. It also discusses a range of optimization methods that have been adopted to solve stochastic problems, as well as stochastic methods for deterministic optimization. Subsequently, areas of overlap between simulation and optimization, in particular optimization-within-MCMC and MCMC-driven optimization are discussed.
Random Designs for Estimating Integrals of Stochastic Processes
Schoenfelder, Carol; Cambanis, Stamatis
1982-01-01
The integral of a second-order stochastic process $Z$ over a $d$-dimensional domain is estimated by a weighted linear combination of observations of $Z$ in a random design. The design sample points are possibly dependent random variables and are independent of the process $Z$, which may be nonstationary. Necessary and sufficient conditions are obtained for the mean squared error of a random design estimator to converge to zero as the sample size increases towards infinity. Simple random, stra...
Stochastic Earthquake Rupture Modeling Using Nonparametric Co-Regionalization
Lee, Kyungbook; Song, Seok Goo
2016-10-01
Accurate predictions of the intensity and variability of ground motions are essential in simulation-based seismic hazard assessment. Advanced simulation-based ground motion prediction methods have been proposed to complement the empirical approach, which suffers from the lack of observed ground motion data, especially in the near-source region for large events. It is important to quantify the variability of the earthquake rupture process for future events and to produce a number of rupture scenario models to capture the variability in simulation-based ground motion predictions. In this study, we improved the previously developed stochastic earthquake rupture modeling method by applying the nonparametric co-regionalization, which was proposed in geostatistics, to the correlation models estimated from dynamically derived earthquake rupture models. The nonparametric approach adopted in this study is computationally efficient and, therefore, enables us to simulate numerous rupture scenarios, including large events (M > 7.0). It also gives us an opportunity to check the shape of true input correlation models in stochastic modeling after being deformed for permissibility. We expect that this type of modeling will improve our ability to simulate a wide range of rupture scenario models and thereby predict ground motions and perform seismic hazard assessment more accurately.
Stochastic Time Models of Syllable Structure
Shaw, Jason A.; Gafos, Adamantios I.
2015-01-01
Drawing on phonology research within the generative linguistics tradition, stochastic methods, and notions from complex systems, we develop a modelling paradigm linking phonological structure, expressed in terms of syllables, to speech movement data acquired with 3D electromagnetic articulography and X-ray microbeam methods. The essential variable in the models is syllable structure. When mapped to discrete coordination topologies, syllabic organization imposes systematic patterns of variability on the temporal dynamics of speech articulation. We simulated these dynamics under different syllabic parses and evaluated simulations against experimental data from Arabic and English, two languages claimed to parse similar strings of segments into different syllabic structures. Model simulations replicated several key experimental results, including the fallibility of past phonetic heuristics for syllable structure, and exposed the range of conditions under which such heuristics remain valid. More importantly, the modelling approach consistently diagnosed syllable structure proving resilient to multiple sources of variability in experimental data including measurement variability, speaker variability, and contextual variability. Prospects for extensions of our modelling paradigm to acoustic data are also discussed. PMID:25996153
Stochastic TDHF in an exactly solvable model
Lacombe, Lionel; Suraud, Eric; Dinh, Phuong Mai
2016-01-01
We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole ($2p2h$) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of $\\Omega$ particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small $\\Omega$. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow $2p2h$ transitions. Limitations concerning low energy excitations and memory effects are also discussed.
Hierarchical Stochastic Simulation Algorithm for SBML Models of Genetic Circuits
Directory of Open Access Journals (Sweden)
Leandro eWatanabe
2014-11-01
Full Text Available This paper describes a hierarchical stochastic simulation algorithm which has been implemented within iBioSim, a tool used to model, analyze, and visualize genetic circuits. Many biological analysis tools flatten out hierarchy before simulation, but there are many disadvantages associated with this approach. First, the memory required to represent the model can quickly expand in the process. Second, the flattening process is computationally expensive. Finally, when modeling a dynamic cellular population within iBioSim, inlining the hierarchy of the model is inefficient since models must grow dynamically over time. This paper discusses a new approach to handle hierarchy on the fly to make the tool faster and more memory-efficient. This approach yields significant performance improvements as compared to the former flat analysis method.
Modeling Departure Time Choice with Stochastic Networks
Li, H.; Bliemer, M.C.J.; Bovy, P.H.L.
2010-01-01
Stochastic supply and fluctuating travel demand lead to stochasticity in travel times and travel costs experienced by travelers from time to time within a day and at the same time from day to day. Many studies show that travel time un-reliability has significant impacts on traveler’s choice behavior
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.
Gompertzian stochastic model with delay effect to cervical cancer growth
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-02-01
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.
Expectation propagation for continuous time stochastic processes
Cseke, Botond; Schnoerr, David; Opper, Manfred; Sanguinetti, Guido
2016-12-01
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.
Unrelated Machine Scheduling with Stochastic Processing Times
Skutella, Martin; Sviridenko, Maxim; Uetz, Marc
2016-01-01
Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the processing times of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated
Unrelated Machine Scheduling with Stochastic Processing Times
Skutella, Martin; Sviridenko, Maxim; Uetz, Marc Jochen
Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the processing times of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated
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.
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 daily modeling of arctic tundra ecosystems
Erler, A.; Epstein, H. E.; Frazier, J.
2011-12-01
ArcVeg is a dynamic vegetation model that has simulated interannual variability of production and abundance of arctic tundra plant types in previous studies. In order to address the effects of changing seasonality on tundra plant community composition and productivity, we have uniquely adapted the model to operate on the daily timescale. Each section of the model-weather generation, nitrogen mineralization, and plant growth dynamics-are driven by daily fluctuations in simulated temperature conditions. These simulation dynamics are achieved by calibrating stochastic iterative loops and mathematical functions with raw field data. Air temperature is the fundamental driver in the model, parameterized by climate data collected in the field across numerous arctic tundra sites, and key daily statistics are extracted (mean and standard deviation of temperature for each day of the year). Nitrogen mineralization is calculated as an exponential function from the simulated temperature. The seasonality of plant growth is driven by the availability of nitrogen and constrained by historical patterns and dynamics of the remotely sensed normalized difference vegetation index (NDVI), as they pertain to the seasonal onset of growth. Here we describe the methods used for daily weather generation, nitrogen mineralization, and the daily competition among twelve plant functional types for nitrogen and subsequent growth. This still rather simple approach to vegetation dynamics has the capacity to generate complex relationships between seasonal patterns of temperature and arctic tundra vegetation community structure and function.
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.
5th Seminar on Stochastic Processes, Random Fields and Applications
Russo, Francesco; Dozzi, Marco
2008-01-01
This volume contains twenty-eight refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 30 to June 3, 2005. The seminar focused mainly on stochastic partial differential equations, random dynamical systems, infinite-dimensional analysis, approximation problems, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance. Contributors: Y. Asai, J.-P. Aubin, C. Becker, M. Benaïm, H. Bessaih, S. Biagini, S. Bonaccorsi, N. Bouleau, N. Champagnat, G. Da Prato, R. Ferrière, F. Flandoli, P. Guasoni, V.B. Hallulli, D. Khoshnevisan, T. Komorowski, R. Léandre, P. Lescot, H. Lisei, J.A. López-Mimbela, V. Mandrekar, S. Méléard, A. Millet, H. Nagai, A.D. Neate, V. Orlovius, M. Pratelli, N. Privault, O. Raimond, M. Röckner, B. Rüdiger, W.J. Runggaldi...
Prediction Theory of Periodically Correlated Stochastic Processes
2015-05-12
in order to do a reliable forecasting of periodically correlated sequences with large period (or continuous time processes) the standard method of...aimed at sequences with large periods. It has been known already for years that in order to do a reliable forecasting of periodically correlated...we showed that this technique is very efficient. We successfully used it to study structure, regularity, autoregressive representation, innovation
Reservoir Stochastic Modeling Constrained by Quantitative Geological Conceptual Patterns
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper discusses the principles of geologic constraints on reservoir stochastic modeling. By using the system science theory, two kinds of uncertainties, including random uncertainty and fuzzy uncertainty, are recognized. In order to improve the precision of stochastic modeling and reduce the uncertainty in realization, the fuzzy uncertainty should be stressed, and the "geological genesis-controlled modeling" is conducted under the guidance of a quantitative geological pattern. An example of the Pingqiao horizontal-well division of the Ansai Oilfield in the Ordos Basin is taken to expound the method of stochastic modeling.
The Stochastic stability of a Logistic model with Poisson white noise
Institute of Scientific and Technical Information of China (English)
Duan Dong-Hai; Xu Wei; Su Jun; Zhou Bing-Chang
2011-01-01
The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised It(o) differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species.
Digital hardware implementation of a stochastic two-dimensional neuron model.
Grassia, F; Kohno, T; Levi, T
2017-02-22
This study explores the feasibility of stochastic neuron simulation in digital systems (FPGA), which realizes an implementation of a two-dimensional neuron model. The stochasticity is added by a source of current noise in the silicon neuron using an Ornstein-Uhlenbeck process. This approach uses digital computation to emulate individual neuron behavior using fixed point arithmetic operation. The neuron model's computations are performed in arithmetic pipelines. It was designed in VHDL language and simulated prior to mapping in the FPGA. The experimental results confirmed the validity of the developed stochastic FPGA implementation, which makes the implementation of the silicon neuron more biologically plausible for future hybrid experiments.
Stochastic Integrals and Processes with Independent Increments.
1985-03-01
bounded variation over every finite La interval. This will be case iff it is the case for all a > 0. The process 4(t), t > 0, will be assumed to be...the sample paths of are of bounded variation over [O,t] with probability one, and so, as Kallenberg noted, one may simple use the Lebesgue-Stieltjes...over (O,t]. Assume further that f IdM(xs) < -, i.e. that almost every path of aJx[0, ti is of bounded variation over [O,t]. Let dlI denote the total
Discrete stochastic processes and optimal filtering
Bertein, Jean-Claude
2012-01-01
Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which ar
A stochastic evolutionary model generating a mixture of exponential distributions
Fenner, Trevor; Levene, Mark; Loizou, George
2016-02-01
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
A stochastic phase-field model determined from molecular dynamics
von Schwerin, Erik
2010-03-17
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.
A Stochastic Evolutionary Growth Model for Social Networks
Fenner, T; Loizou, G; Roussos, G; Fenner, Trevor; Levene, Mark; Loizou, George; Roussos, George
2006-01-01
We present a stochastic model for a social network, where new actors may join the network, existing actors may become inactive and, at a later stage, reactivate themselves. Our model captures the evolution of the network, assuming that actors attain new relations or become active according to the preferential attachment rule. We derive the mean-field equations for this stochastic model and show that, asymptotically, the distribution of actors obeys a power-law distribution. In particular, the model applies to social networks such as wireless local area networks, where users connect to access-points, and peer-to-peer networks where users connect to each other. As a proof of concept, we demonstrate the validity of our model empirically by analysing a public log containing traces from a wireless network at Dartmouth College over a period of three years. Analysing the data processed according to our model, we demonstrate that the distribution of user accesses is asymptotically a power-law distribution.
Systematic parameter inference in stochastic mesoscopic modeling
Lei, Huan; Yang, Xiu; Li, Zhen; Karniadakis, George Em
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.
Multitime correlation functions in nonclassical stochastic processes
Krumm, F.; Sperling, J.; Vogel, W.
2016-06-01
A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent P functional that generalizes the Glauber-Sudarshan P function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.
Coppola, Antonio; Comegna, Alessandro; Dragonetti, Giovanna; Lamaddalena, Nicola; Zdruli, Pandi
2013-04-01
modelling approaches have been developed at small space scales. Their extension to the applicative macroscale of the regional model is not a simple task mainly because of the heterogeneity of vadose zone properties, as well as of non-linearity of hydrological processes. Besides, one of the problems when applying distributed models is that spatial and temporal scales for data to be used as input in the models vary on a wide range of scales and are not always consistent with the model structure. Under these conditions, a strictly deterministic response to questions about the fate of a pollutant in the soil is impossible. At best, one may answer "this is the average behaviour within this uncertainty band". Consequently, the extension of these equations to account for regional-scale processes requires the uncertainties of the outputs be taken into account if the pollution vulnerability maps that may be drawn are to be used as agricultural management tools. A map generated without a corresponding map of associated uncertainties has no real utility. The stochastic stream tube approach is a frequently used to the water flux and solute transport through the vadose zone at applicative scales. This approach considers the field soil as an ensemble of parallel and statistically independent tubes, assuming only vertical flow. The stream tubes approach is generally used in a probabilistic framework. Each stream tube defines local flow properties that are assumed to vary randomly between the different stream tubes. Thus, the approach allows average water and solute behaviour be described, along with the associated uncertainty bands. These stream tubes are usually considered to have parameters that are vertically homogeneous. This would be justified by the large difference between the horizontal and vertical extent of the spatial applicative scale. Vertical is generally overlooked. Obviously, all the model outputs are conditioned by this assumption. The latter, in turn, is more dictated by
Jędrak, Jakub
2016-01-01
We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g. oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the RC low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones. We also demonstrate that the $n$-th cumulant of the protein number distribution depends on the $n$-th moment of the burst size distribution. We use these results to show that different measures of noise (coefficient of variation, Fano factor, fractional change of varian...
System Design Support by Optimization Method Using Stochastic Process
Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio
We proposed the new optimization method based on stochastic process. The characteristics of this method are to obtain the approximate solution of the optimum solution as an expected value. In numerical calculation, a kind of Monte Carlo method is used to obtain the solution because of stochastic process. Then, it can obtain the probability distribution of the design variable because it is generated in the probability that design variables were in proportion to the evaluation function value. This probability distribution shows the influence of design variables on the evaluation function value. This probability distribution is the information which is very useful for the system design. In this paper, it is shown the proposed method is useful for not only the optimization but also the system design. The flight trajectory optimization problem for the hang-glider is shown as an example of the numerical calculation.
Supersymmetric Theory of Stochastic ABC Model: A Numerical Study
Ovchinnikov, Igor V; Ensslin, Torsten A; Wang, Kang L
2016-01-01
In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics (STS). STS characterises stochastic differential equations (SDEs) by the spectrum of the stochastic evolution operator (SEO) on elements of the exterior algebra or differentials forms over the system's phase space, X. STS can thereby classify SDEs as chaotic or non-chaotic by identifying the phenomenon of stochastic chaos with the spontaneously broken topological supersymmetry that all SDEs possess. We demonstrate the following three properties of the SEO, deduced previously analytically and from physical arguments: the SEO spectra for zeroth and top degree forms never break topological supersymmetry, all SDEs possesses pseudo-time-reversal symmetry, and each de Rahm cohomology class provides one supersymmetric eigenstate. Our results also suggests that the SEO spectra for forms of complementary degrees, i.e., k and ...
Generation of a stochastic precipitation model for the tropical climate
Ng, Jing Lin; Abd Aziz, Samsuzana; Huang, Yuk Feng; Wayayok, Aimrun; Rowshon, MK
2017-06-01
A tropical country like Malaysia is characterized by intense localized precipitation with temperatures remaining relatively constant throughout the year. A stochastic modeling of precipitation in the flood-prone Kelantan River Basin is particularly challenging due to the high intermittency of precipitation events of the northeast monsoons. There is an urgent need to have long series of precipitation in modeling the hydrological responses. A single-site stochastic precipitation model that includes precipitation occurrence and an intensity model was developed, calibrated, and validated for the Kelantan River Basin. The simulation process was carried out separately for each station without considering the spatial correlation of precipitation. The Markov chains up to the fifth-order and six distributions were considered. The daily precipitation data of 17 rainfall stations for the study period of 1954-2013 were selected. The results suggested that second- and third-order Markov chains were suitable for simulating monthly and yearly precipitation occurrences, respectively. The fifth-order Markov chain resulted in overestimation of precipitation occurrences. For the mean, distribution, and standard deviation of precipitation amounts, the exponential, gamma, log-normal, skew normal, mixed exponential, and generalized Pareto distributions performed superiorly. However, for the extremes of precipitation, the exponential and log-normal distributions were better while the skew normal and generalized Pareto distributions tend to show underestimations. The log-normal distribution was chosen as the best distribution to simulate precipitation amounts. Overall, the stochastic precipitation model developed is considered a convenient tool to simulate the characteristics of precipitation in the Kelantan River Basin.
Schmidt, Deena R; Thomas, Peter J
2014-04-17
Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion-channel models, such as the Hodgkin-Huxley or other conductance-based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion-channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Galán's approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process.
Ohlberger, Jan; Rogers, Lauren A; Stenseth, Nils Chr
2014-01-01
A persistent debate in population ecology concerns the relative importance of environmental stochasticity and density dependence in determining variability in adult year-class strength, which contributes to future reproduction as well as potential yield in exploited populations. Apart from the strength of the processes, the timing of density regulation may affect how stochastic variation, for instance through climate, translates into changes in adult abundance. In this study, we develop a life-cycle model for the population dynamics of a large marine fish population, Northeast Arctic cod, to disentangle the effects of density-independent and density-dependent processes on early life-stages, and to quantify the strength of compensatory density dependence in the population. The model incorporates information from scientific surveys and commercial harvest, and dynamically links multiple effects of intrinsic and extrinsic factors on all life-stages, from eggs to spawners. Using a state-space approach we account for observation error and stochasticity in the population dynamics. Our findings highlight the importance of density-dependent survival in juveniles, indicating that this period of the life cycle largely determines the compensatory capacity of the population. Density regulation at the juvenile life-stage dampens the impact of stochastic processes operating earlier in life such as environmental impacts on the production of eggs and climate-dependent survival of larvae. The timing of stochastic versus regulatory processes thus plays a crucial role in determining variability in adult abundance. Quantifying the contribution of environmental stochasticity and compensatory mechanisms in determining population abundance is essential for assessing population responses to climate change and exploitation by humans.
Processing in (linear) systems with stochastic input
Nutu, Catalin Silviu; Axinte, Tiberiu
2016-12-01
The paper is providing a different approach to real-world systems, such as micro and macro systems of our real life, where the man has little or no influence on the system, either not knowing the rules of the respective system or not knowing the input of the system, being thus mainly only spectator of the system's output. In such a system, the input of the system and the laws ruling the system could be only "guessed", based on intuition or previous knowledge of the analyzer of the respective system. But, as we will see in the paper, it exists also another, more theoretical and hence scientific way to approach the matter of the real-world systems, and this approach is mostly based on the theory related to Schrödinger's equation and the wave function associated with it and quantum mechanics as well. The main results of the paper are regarding the utilization of the Schrödinger's equation and related theory but also of the Quantum mechanics, in modeling real-life and real-world systems.
Stochastic waves in a Brusselator model with nonlocal interaction.
Biancalani, Tommaso; Galla, Tobias; McKane, Alan J
2011-08-01
We show that intrinsic noise can induce spatiotemporal phenomena such as Turing patterns and traveling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these stochastic waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the stochastic waves analytically and the outcome is tested successfully against simulations. We discuss the possibility that nonlocal models in other areas, such as epidemic spread or social dynamics, may contain similar stochastically induced patterns.
Stochastic simulations of cargo transport by processive molecular motors.
Korn, Christian B; Klumpp, Stefan; Lipowsky, Reinhard; Schwarz, Ulrich S
2009-12-28
We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.
Kinetic theory of age-structured stochastic birth-death processes
Greenman, Chris D.; Chou, Tom
2016-01-01
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.
A stochastic evolutionary model for capturing human dynamics
Fenner, Trevor; Loizou, George
2015-01-01
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. We derive a general solution for the model in the form of a product, and then a continuous approximation to the solution via the renewal equation describing age-structured population dynamics. This enables us to model a wide rage of survival distributions, according to the choice of the mortality distribution. We provide empirical evidence for the validity of the model from a longitudinal data set of popular search engine queries over 114 months, showing that the survival function of these queries is closely matched by the solution for our model with power-law mortality.
Markov Regime Switching of Stochastic Volatility Lévy Model on Approximation Mode
Directory of Open Access Journals (Sweden)
Arthit Intarasit
2013-01-01
Full Text Available This paper deals with financial modeling to describe the behavior of asset returns, through consideration of economic cycles together with the stylized empirical features of asset returns such as fat tails. We propose that asset returns are modeled by a stochastic volatility Lévy process incorporating a regime switching model. Based on the risk-neutral approach, there exists a large set of candidates of martingale measures due to the driving of a stochastic volatility Lévy process in the proposed model which renders the market incomplete in general. We first establish an equivalent martingale measure for the proposed model introduced in risk-neutral version. Regime switching of stochastic volatility Lévy process is employed in an approximation mode for model calibration and the calibration of parameters model done based on EM algorithm. Finally, some empirical results are illustrated via applications to the Bangkok Stock Exchange of Thailand index.
Dynamic stochastic optimization models for air traffic flow management
Mukherjee, Avijit
This dissertation presents dynamic stochastic optimization models for Air Traffic Flow Management (ATFM) that enables decisions to adapt to new information on evolving capacities of National Airspace System (NAS) resources. Uncertainty is represented by a set of capacity scenarios, each depicting a particular time-varying capacity profile of NAS resources. We use the concept of a scenario tree in which multiple scenarios are possible initially. Scenarios are eliminated as possibilities in a succession of branching points, until the specific scenario that will be realized on a particular day is known. Thus the scenario tree branching provides updated information on evolving scenarios, and allows ATFM decisions to be re-addressed and revised. First, we propose a dynamic stochastic model for a single airport ground holding problem (SAGHP) that can be used for planning Ground Delay Programs (GDPs) when there is uncertainty about future airport arrival capacities. Ground delays of non-departed flights can be revised based on updated information from scenario tree branching. The problem is formulated so that a wide range of objective functions, including non-linear delay cost functions and functions that reflect equity concerns can be optimized. Furthermore, the model improves on existing practice by ensuring efficient use of available capacity without necessarily exempting long-haul flights. Following this, we present a methodology and optimization models that can be used for decentralized decision making by individual airlines in the GDP planning process, using the solutions from the stochastic dynamic SAGHP. Airlines are allowed to perform cancellations, and re-allocate slots to remaining flights by substitutions. We also present an optimization model that can be used by the FAA, after the airlines perform cancellation and substitutions, to re-utilize vacant arrival slots that are created due to cancellations. Finally, we present three stochastic integer programming
组织决策过程的随机有色Petri网模型%A Stochastic Colored Petri Net Model of Organization Decision Making Process
Institute of Scientific and Technical Information of China (English)
李文波; 吴冲锋; 王意冈
2001-01-01
随机有色Petri网可为组织决策过程提供描述框架和分析手段。基于SCPN的计算机图形建模仿真工具研究组织设计变量对组织决策效率的影响，这些变量包括决策人之间的协调结构、决策人偏好、决策方法、决策目标数、备选方案数等。仿真实例结果表明，决策人之间的协调结构对决策效率有明显的影响。%Stochastic Colored Petri Net(SCPN) is used as a descriptive framework and analysis instrument of organization decision making. A SCPN-based computer graphic modeling and simulating software is developed to study the impact of the organizational design variables on organization decision making efficiency. These variables include decision making coordination structure, preference of decision makers, decision making method, number of decision making properties, and number of alternatives. The simulation result indicates that decision making coordination structure has significant influence on decision making efficiency.
Determining Reduced Order Models for Optimal Stochastic Reduced Order Models
Energy Technology Data Exchange (ETDEWEB)
Bonney, Matthew S. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Brake, Matthew R.W. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2015-08-01
The use of parameterized reduced order models(PROMs) within the stochastic reduced order model (SROM) framework is a logical progression for both methods. In this report, five different parameterized reduced order models are selected and critiqued against the other models along with truth model for the example of the Brake-Reuss beam. The models are: a Taylor series using finite difference, a proper orthogonal decomposition of the the output, a Craig-Bampton representation of the model, a method that uses Hyper-Dual numbers to determine the sensitivities, and a Meta-Model method that uses the Hyper-Dual results and constructs a polynomial curve to better represent the output data. The methods are compared against a parameter sweep and a distribution propagation where the first four statistical moments are used as a comparison. Each method produces very accurate results with the Craig-Bampton reduction having the least accurate results. The models are also compared based on time requirements for the evaluation of each model where the Meta- Model requires the least amount of time for computation by a significant amount. Each of the five models provided accurate results in a reasonable time frame. The determination of which model to use is dependent on the availability of the high-fidelity model and how many evaluations can be performed. Analysis of the output distribution is examined by using a large Monte-Carlo simulation along with a reduced simulation using Latin Hypercube and the stochastic reduced order model sampling technique. Both techniques produced accurate results. The stochastic reduced order modeling technique produced less error when compared to an exhaustive sampling for the majority of methods.
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.
Stochastic models for spike trains of single neurons
Sampath, G
1977-01-01
1 Some basic neurophysiology 4 The neuron 1. 1 4 1. 1. 1 The axon 7 1. 1. 2 The synapse 9 12 1. 1. 3 The soma 1. 1. 4 The dendrites 13 13 1. 2 Types of neurons 2 Signals in the nervous system 14 2. 1 Action potentials as point events - point processes in the nervous system 15 18 2. 2 Spontaneous activi~ in neurons 3 Stochastic modelling of single neuron spike trains 19 3. 1 Characteristics of a neuron spike train 19 3. 2 The mathematical neuron 23 4 Superposition models 26 4. 1 superposition of renewal processes 26 4. 2 Superposition of stationary point processe- limiting behaviour 34 4. 2. 1 Palm functions 35 4. 2. 2 Asymptotic behaviour of n stationary point processes superposed 36 4. 3 Superposition models of neuron spike trains 37 4. 3. 1 Model 4. 1 39 4. 3. 2 Model 4. 2 - A superposition model with 40 two input channels 40 4. 3. 3 Model 4. 3 4. 4 Discussion 41 43 5 Deletion models 5. 1 Deletion models with 1nd~endent interaction of excitatory and inhibitory sequences 44 VI 5. 1. 1 Model 5. 1 The basic de...
Minimum Uncertainty, Coherence and Squeezing in Diffusion Processes, and Stochastic Quantization
De Martino, S; Illuminati, F; Vitiello, G; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio; Vitiello, Giuseppe
1993-01-01
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
Stochastic equations, flows and measure-valued processes
Dawson, Donald A
2010-01-01
We first prove some general results on pathwise uniqueness, comparison property and existence of non-negative strong solutions of stochastic equations driven by white noises and Poisson random measures. The results are then used to prove the strong existence of two classes of stochastic flows associated with coalescents with multiple collisions, that is, generalized Fleming-Viot flows and flows of continuous-state branching processes with immigration. One of them unifies the different treatments of three kinds of flows in Bertoin and Le Gall (2005). Two scaling limit theorems for the generalized Fleming-Viot flows are proved, which lead to sub-critical branching immigration superprocesses. {From} those theorems we derive easily a generalization of the limit theorem for finite point motions of the flows in Bertoin and Le Gall (2006).
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1981-04-01
Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1980-01-01
Digitally generated solutions of nonlinear stochastic systems are not unique, but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system, but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions resulting from different integration algorithms and comparing the moments to those arising from various stochastic integral definitions. Monte Carlo simulations and statistical tests are applied to illustrate the determining role that computational procedures play in generating solutions. This algorithm dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases, in which unique solutions are determined by any convergent numerical algorithm. Consequences of this relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. 2 figures.
Some Algorithms to Identify Rational Structures in Stochastic Processes with Expectations
Directory of Open Access Journals (Sweden)
Concepción González-Concepción
2007-01-01
Full Text Available This research was concerned with the identification of rational models in stochastic processes and we use the Padé-Laurent Approximation to identify a Transfer-Function Model with Expectations. We mention the T-table method and focus in studying the generalised epsilon-algorithm, emphasizing the main role of the statistical significance of their numerical entries. Empirical work is made for non-causal TF models using both simulated and economic real data.
Explicit calibration and simulation of stochastic fields by low-order ARMA processes
DEFF Research Database (Denmark)
Krenk, Steen
2011-01-01
A simple framework for autoregressive simulation of stochastic fields is presented. The autoregressive format leads to a simple exponential correlation structure in the time-dimension. In the case of scalar processes a more detailed correlation structure can be obtained by adding memory to the pr......A simple framework for autoregressive simulation of stochastic fields is presented. The autoregressive format leads to a simple exponential correlation structure in the time-dimension. In the case of scalar processes a more detailed correlation structure can be obtained by adding memory......-space' variables in the simulation. For a scalar process this would imply an increase of the dimension of the process to be simulated. In the case of a stochastic field the correlation in the time-dimension is represented, although indirectly, in the simultaneous spatial correlation. The model with the shortest...... memory -the single-step autoregressive model - is analyzed in detail, and an efficient multi-step calibration procedure is developed. The calibration makes direct use of conditional correlations and means, expressed explicitly in terms of the zero and k-step correlation matrices of the stochastic field...
Mathematical modeling and stochastic simulation of soft materials
Zeng, Yun
Soft materials are all around us; they may appear as consumer products, foods, or biological materials. The interest in studying the properties of soft materials both experimentally and theoretically has steadily increased due to their wide range of industrial applications. One example of a soft material is wormlike micellar solutions. Depending on the temperature and composition, these solvent-surfactant-salt mixtures may exhibit close to mono-exponential or, alternatively, power-law or stretched-exponential stress decay. Of particular interest to this thesis is the development of stochastic models that can capture the stress relaxation behavior of such materials in the small strain limit, which is non-exponential in time as opposed to exponential. Continuous time random walk (CTRW) or subordinated Langevin processes are utilized to model systems exhibiting non-exponential relaxation behavior or anomalous diffusion. Stochastic simulations using the CTRW approach or the subordination method are carried out in this thesis for one-dimensional systems in which the probability density distribution of particle positions is described by a fractional Fokker-Planck equation (FFPE). The equivalence of the CTRW simulation and the subordination simulation with that of the FFPE is analyzed through the simulation of an ensemble of particle trajectories. The simulated particle dynamics suggest that CTRW processes or subordinated Langevin dynamics can be included in soft material mesoscale dynamics to capture the anomalous transport. To model the non-exponential stress relaxation dynamics of soft gel systems (three-dimensional fluids), stochastic models are simulated using transient network theory as developed and combined with the CTRW and subordinated Langevin processes. This approach enables us to connect the microstructural dynamics of certain soft gel-like materials with macroscale experimental observations by examining the material properties under homogeneous shear flow
A stochastic model of ant trail following with two pheromones
Malíčková, Miriam; Boďová, Katarína
2015-01-01
Colonies of ants are systems of interacting living organisms in which interactions between individuals and their environment can produce a reliable performance of a complex tasks without the need for centralised control. Particularly remarkable is the process of formation of refined paths between the nest and food sources that is essential for successful foraging. We have designed a simple stochastic off-lattice model of ant foraging in the absence of direct communication. The motion of ants is governed by two components - a random change in direction of motion that improves ability to explore the environment (facilitating food discovery), and a non-random global indirect interaction component based on pheromone signalling. Using numerical simulations we have studied the model behaviour in different parameter regimes and tested the ability of our model ants to adapt to changes in the external environment. The simulated behaviour of ants in the model recapitulated the experimentally observed behaviours of real...
Whole-field visual motion drives swimming in larval zebrafish via a stochastic process.
Portugues, Ruben; Haesemeyer, Martin; Blum, Mirella L; Engert, Florian
2015-05-01
Caudo-rostral whole-field visual motion elicits forward locomotion in many organisms, including larval zebrafish. Here, we investigate the dependence on the latency to initiate this forward swimming as a function of the speed of the visual motion. We show that latency is highly dependent on speed for slow speeds (1.5 s, which is much longer than neuronal transduction processes. What mechanisms underlie these long latencies? We propose two alternative, biologically inspired models that could account for this latency to initiate swimming: an integrate and fire model, which is history dependent, and a stochastic Poisson model, which has no history dependence. We use these models to predict the behavior of larvae when presented with whole-field motion of varying speed and find that the stochastic process shows better agreement with the experimental data. Finally, we discuss possible neuronal implementations of these models.
Overwinding in a stochastic model of an extended polymer
Energy Technology Data Exchange (ETDEWEB)
Bernido, Christopher C. [Research Center for Theoretical Physics, Central Visayan Institute Foundation, Jagna, Bohol 6308 (Philippines)], E-mail: cbernido@mozcom.com; Carpio-Bernido, M. Victoria [Research Center for Theoretical Physics, Central Visayan Institute Foundation, Jagna, Bohol 6308 (Philippines)
2007-09-10
We evaluate explicit expressions of length-dependent winding configuration probabilities for a biopolymer. The stochastic model incorporates several experimentally observed features. In particular, it exhibits overwinding under stretching forces until a critical length of the polymer is reached.
Jedrak, Jakub; Ochab-Marcinek, Anna
2016-09-01
We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g., oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the resistor-capacitor low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones. We also demonstrate that the n th cumulant of the protein number distribution depends on the n th moment of the burst size distribution. We use these results to show that different measures of noise (coefficient of variation, Fano factor, fractional change of variance) may vary in time in a different manner. Therefore, any biological hypothesis of evolutionary optimization based on the nonmonotonic dependence of a chosen measure of noise on time must justify why it assumes that biological evolution quantifies noise in that particular way. Finally, we show that not only for exponentially distributed burst sizes but also for a wider class of burst size distributions (e.g., Dirac delta and gamma) the control of gene expression level by burst frequency modulation gives rise to proportional scaling of variance of the protein number distribution to its mean, whereas the control by amplitude modulation implies proportionality of protein number variance to the mean squared.
Generalized Fleming-Viot processes with immigration via stochastic flows of partitions
Foucart, Clément
2011-01-01
The generalized Fleming-Viot processes were defined in 1999 by Donnelly and Kurtz using a particle model and by Bertoin and Le Gall in 2003 using stochastic flows of bridges. In both methods, the key argument used to characterize these processes is the duality between these processes and exchangeable coalescents. A larger class of coalescent processes, called distinguished coalescents, was set up recently to incorporate an immigration phenomenon in the underlying population. The purpose of this article is to define and characterize a class of probability-measure valued processes called the generalized Fleming-Viot processes with immigration. We consider some stochastic flows of partitions of Z_{+}, in the same spirit as Bertoin and Le Gall's flows, replacing roughly speaking, composition of bridges by coagulation of partitions. Identifying at any time a population with the integers $\\mathbb{N}:=\\{1,2,...\\}$, the formalism of partitions is effective in the past as well as in the future especially when there ar...
Stochastic modeling of kHz quasi-periodic oscillation light curves
DEFF Research Database (Denmark)
Vio, R.; Rebusco, P.; Andreani, P.
2006-01-01
" deterministic form. In the present paper the same model is considered. The equation are numerically integrated, dropping the ad hoc forcing and adding instead a stochastic term to mimic the action of the very complex processes that occur in accretion disks as, for example, MRI turbulence. We demonstrate...... that the presence of the stochastic term is able to trigger the resonance in epicyclic oscillations of nearly Keplerian disks, and it influences their pattern...
Stochastic kinetic models: Dynamic independence, modularity and graphs
Bowsher, Clive G
2010-01-01
The dynamic properties and independence structure of stochastic kinetic models (SKMs) are analyzed. An SKM is a highly multivariate jump process used to model chemical reaction networks, particularly those in biochemical and cellular systems. We identify SKM subprocesses with the corresponding counting processes and propose a directed, cyclic graph (the kinetic independence graph or KIG) that encodes the local independence structure of their conditional intensities. Given a partition $[A,D,B]$ of the vertices, the graphical separation $A\\perp B|D$ in the undirected KIG has an intuitive chemical interpretation and implies that $A$ is locally independent of $B$ given $A\\cup D$. It is proved that this separation also results in global independence of the internal histories of $A$ and $B$ conditional on a history of the jumps in $D$ which, under conditions we derive, corresponds to the internal history of $D$. The results enable mathematical definition of a modularization of an SKM using its implied dynamics. Gra...
Stochastic Parameterization: Towards a new view of Weather and Climate Models
Berner, Judith; Batte, Lauriane; De La Camara, Alvaro; Crommelin, Daan; Christensen, Hannah; Colangeli, Matteo; Dolaptchiev, Stamen; Franzke, Christian L E; Friederichs, Petra; Imkeller, Peter; Jarvinen, Heikki; Juricke, Stephan; Kitsios, Vassili; Lott, Franois; Lucarini, Valerio; Mahajan, Salil; Palmer, Timothy N; Penland, Cecile; Von Storch, Jin-Song; Sakradzija, Mirjana; Weniger, Michael; Weisheimer, Antje; Williams, Paul D; Yano, Jun-Ichi
2015-01-01
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal ensembles: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy and improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides more skillful estimates of uncertainty, but is also extremely promising for reducing longstanding climate biases and relevant for determining the climate response to forcings such as e.g., an increase of CO2. This article highlights recent results from different research groups which show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface and cryosphere of comprehensive weather and climate models a) gives rise to more reliable probabilistic forecasts of weather and climate and b) reduces systematic model bias. We make a case that the use of mathematically ...
StochPy: a comprehensive, user-friendly tool for simulating stochastic biological processes.
Directory of Open Access Journals (Sweden)
Timo R Maarleveld
Full Text Available Single-cell and single-molecule measurements indicate the importance of stochastic phenomena in cell biology. Stochasticity creates spontaneous differences in the copy numbers of key macromolecules and the timing of reaction events between genetically-identical cells. Mathematical models are indispensable for the study of phenotypic stochasticity in cellular decision-making and cell survival. There is a demand for versatile, stochastic modeling environments with extensive, preprogrammed statistics functions and plotting capabilities that hide the mathematics from the novice users and offers low-level programming access to the experienced user. Here we present StochPy (Stochastic modeling in Python, which is a flexible software tool for stochastic simulation in cell biology. It provides various stochastic simulation algorithms, SBML support, analyses of the probability distributions of molecule copy numbers and event waiting times, analyses of stochastic time series, and a range of additional statistical functions and plotting facilities for stochastic simulations. We illustrate the functionality of StochPy with stochastic models of gene expression, cell division, and single-molecule enzyme kinetics. StochPy has been successfully tested against the SBML stochastic test suite, passing all tests. StochPy is a comprehensive software package for stochastic simulation of the molecular control networks of living cells. It allows novice and experienced users to study stochastic phenomena in cell biology. The integration with other Python software makes StochPy both a user-friendly and easily extendible simulation tool.
Institute of Scientific and Technical Information of China (English)
周炳海; 翟子青
2011-01-01
以随机过程理论为基础,结合实验数据和分析结果,提出了基于非齐次Poisson过程和非定态Gamma过程的点蚀萌发和生长建模方法,建立了一套系统的关于镍基690合金蒸汽发生器传热管点蚀失效的实验方法、建模方法和仿真方法,对由点蚀引起的镍基690合金蒸汽发生器传热管破损失效的衰退过程进行了有效仿真,得到了不同工作环境下镍基690合金蒸汽发生器传热管的寿命概率分布.结果表明,在不考虑传热管内具体流体动力学和辐照因素的前提下,本文建立的点蚀引起的衰退过程模型可有效地模拟镍基690合金蒸汽发生器传热管的点蚀萌发和生长,对预测其寿命和制定相关的维修计划具有重要的参考价值.%Pitting corrosion is one of the most serious modes of localized corrosions that can cause deteriorations of Ni-based alloy 690 steam generator tubes. Because the initiation and propagation of pitting are subject to interactions of different factors, it is a stochastic process. It is almost impossible to draw any deterministic models for formations of the processes. To efficiently model the formation process of pitting, firstly, experimental schemes of pitting formations were designed. Based on stochastic theory, combined experimental data and analyzing results, a modeling method was presented with stochastic processes. Namely, non-homogeneous Poisson process (NHPP) was used to model the pitting initiation process and non-stationary Gamma model was used to set up pitting propagation model. A systemic method was built for pitting corrosion failure of the Ni-based alloy 690 tubes, including experimental method, modeling method and simulation method. Finally, the stochastic degradation failure of the Ni-based alloy 690 tubes was simulated. The probability distribution of the lifespan of the Ni-based alloy 690 tubes was obtained under different working environments. The results showed that the proposed
Theory of Selection Operators on Hyperspaces and Multivalued Stochastic Processes
Institute of Scientific and Technical Information of China (English)
高勇; 张文修
1994-01-01
In this paper, a new concept of selection operators on hyperspaces (subsets spaces) is introduced, and the existence theorems for several kinds of selection operators are proved. Using the methods of selection operators, we give a selection characterization of identically distributed multivalued random variables and completely solve the vector-valued selection problem for sequences of multivalued random variables converging in distribution. The regular selections and Markov selections for multivalued stochastic processes are studied, and a discretization theorem for multivalued Markov processes is established. A theorem on the asymptotic martingale selections for compact and convex multivalued asymptotic martingale is proved.
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.
Excitability in a stochastic differential equation model for calcium puffs.
Rüdiger, S
2014-06-01
Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.
Kinetic and Stochastic Models of 1D yeast ``prions"
Kunes, Kay
2005-03-01
Mammalian prion proteins (PrP) are of public health interest because of mad cow and chronic wasting diseases. Yeasts have proteins, which can undergo similar reconformation and aggregation processes to PrP; yeast ``prions" are simpler to experimentally study and model. Recent in vitro studies of the SUP35 protein (1), showed long aggregates and pure exponential growth of the misfolded form. To explain this data, we have extended a previous model of aggregation kinetics along with our own stochastic approach (2). Both models assume reconformation only upon aggregation, and include aggregate fissioning and an initial nucleation barrier. We find for sufficiently small nucleation rates or seeding by small dimer concentrations that we can achieve the requisite exponential growth and long aggregates.
Baselga, Andrés; Bonthoux, Sébastien; Balent, Gérard
2015-01-01
Temporal variation in the composition of species assemblages could be the result of deterministic processes driven by environmental change and/or stochastic processes of colonization and local extinction. Here, we analyzed the relative roles of deterministic and stochastic processes on bird assemblages in an agricultural landscape of southwestern France. We first assessed the impact of land cover change that occurred between 1982 and 2007 on (i) the species composition (presence/absence) of bird assemblages and (ii) the spatial pattern of taxonomic beta diversity. We also compared the observed temporal change of bird assemblages with a null model accounting for the effect of stochastic dynamics on temporal beta diversity. Temporal assemblage dissimilarity was partitioned into two separate components, accounting for the replacement of species (i.e. turnover) and for the nested species losses (or gains) from one time to the other (i.e. nestedness-resultant dissimilarity), respectively. Neither the turnover nor the nestedness-resultant components of temporal variation were accurately explained by any of the measured variables accounting for land cover change (r(2)turnover and 13% of sites for nestedness-resultant dissimilarity. Taken together, our results suggest that land cover change in this agricultural landscape had little impact on temporal beta diversity of bird assemblages. Although other unmeasured deterministic process could be driving the observed patterns, it is also possible that the observed changes in presence/absence species composition of local bird assemblages might be the consequence of stochastic processes in which species populations appeared and disappeared from specific localities in a random-like way. Our results might be case-specific, but if stochastic dynamics are generally dominant, the ability of correlative and mechanistic models to predict land cover change effects on species composition would be compromised.
DEFF Research Database (Denmark)
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode
2009-01-01
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......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...
Stochastic mutualism model with Lévy jumps
Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed
2017-02-01
In this paper, we consider a stochastic mutualism model with Lévy jumps. First of all, we show that the positive solution of the system is stochastically ultimate bounded. Then under a simple assumption, we establish sufficient and necessary conditions for the stochastic permanence and extinction of the system. The results show an important property of the Lévy jumps: they are unfavorable for the permanence of the species. Moreover, when there are no Lévy jumps, we show that there is a unique ergodic stationary distribution of the corresponding system under certain conditions. Some numerical simulations are introduced to validate the theoretical results.
Modelling Chinese Smart Grid: A Stochastic Model Checking Case Study
Yüksel, Ender; Nielson, Flemming; Zhu, Huibiao; Huang, Heqing
2012-01-01
Cyber-physical systems integrate information and communication technology functions to the physical elements of a system for monitoring and controlling purposes. The conversion of traditional power grid into a smart grid, a fundamental example of a cyber-physical system, raises a number of issues that require novel methods and applications. In this context, an important issue is the verification of certain quantitative properties of the system. In this technical report, we consider a specific Chinese Smart Grid implementation and try to address the verification problem for certain quantitative properties including performance and battery consumption. We employ stochastic model checking approach and present our modelling and analysis study using PRISM model checker.
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.
Large scale stochastic spatio-temporal modelling with PCRaster
Karssenberg, Derek; Drost, Niels; Schmitz, Oliver; de Jong, Kor; Bierkens, Marc F. P.
2013-04-01
PCRaster is a software framework for building spatio-temporal models of land surface processes (http://www.pcraster.eu). Building blocks of models are spatial operations on raster maps, including a large suite of operations for water and sediment routing. These operations are available to model builders as Python functions. The software comes with Python framework classes providing control flow for spatio-temporal modelling, Monte Carlo simulation, and data assimilation (Ensemble Kalman Filter and Particle Filter). Models are built by combining the spatial operations in these framework classes. This approach enables modellers without specialist programming experience to construct large, rather complicated models, as many technical details of modelling (e.g., data storage, solving spatial operations, data assimilation algorithms) are taken care of by the PCRaster toolbox. Exploratory modelling is supported by routines for prompt, interactive visualisation of stochastic spatio-temporal data generated by the models. The high computational requirements for stochastic spatio-temporal modelling, and an increasing demand to run models over large areas at high resolution, e.g. in global hydrological modelling, require an optimal use of available, heterogeneous computing resources by the modelling framework. Current work in the context of the eWaterCycle project is on a parallel implementation of the modelling engine, capable of running on a high-performance computing infrastructure such as clusters and supercomputers. Model runs will be distributed over multiple compute nodes and multiple processors (GPUs and CPUs). Parallelization will be done by parallel execution of Monte Carlo realizations and sub regions of the modelling domain. In our approach we use multiple levels of parallelism, improving scalability considerably. On the node level we will use OpenCL, the industry standard for low-level high performance computing kernels. To combine multiple nodes we will use
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.
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.
Stochastic von Bertalanffy models, with applications to fish recruitment.
Lv, Qiming; Pitchford, Jonathan W
2007-02-21
We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.
Llopis-Albert, C.; Capilla, J. E.
2010-09-01
SummaryMajor factors affecting groundwater flow through fractured rocks include the geometry of each fracture, its properties and the fracture-network connectivity together with the porosity and conductivity of the rock matrix. When modelling fractured rocks this is translated into attaining a characterization of the hydraulic conductivity ( K) as adequately as possible, despite its high heterogeneity. This links with the main goal of this paper, which is to present an improvement of a stochastic inverse model, named as Gradual Conditioning (GC) method, to better characterise K in a fractured rock medium by considering different K stochastic structures, belonging to independent K statistical populations (SP) of fracture families and the rock matrix, each one with its own statistical properties. The new methodology is carried out by applying independent deformations to each SP during the conditioning process for constraining stochastic simulations to data. This allows that the statistical properties of each SPs tend to be preserved during the iterative optimization process. It is worthwhile mentioning that so far, no other stochastic inverse modelling technique, with the whole capabilities implemented in the GC method, is able to work with a domain covered by several different stochastic structures taking into account the independence of different populations. The GC method is based on a procedure that gradually changes an initial K field, which is conditioned only to K data, to approximate the reproduction of other types of information, i.e., piezometric head and solute concentration data. The approach is applied to the Äspö Hard Rock Laboratory (HRL) in Sweden, where, since the middle nineties, many experiments have been carried out to increase confidence in alternative radionuclide transport modelling approaches. Because the description of fracture locations and the distribution of hydrodynamic parameters within them are not accurate enough, we address the
Methodology Aspects of Quantifying Stochastic Climate Variability with Dynamic Models
Nuterman, Roman; Jochum, Markus; Solgaard, Anna
2015-04-01
The paleoclimatic records show that climate has changed dramatically through time. For the past few millions of years it has been oscillating between ice ages, with large parts of the continents covered with ice, and warm interglacial periods like the present one. It is commonly assumed that these glacial cycles are related to changes in insolation due to periodic changes in Earth's orbit around Sun (Milankovitch theory). However, this relationship is far from understood. The insolation changes are so small that enhancing feedbacks must be at play. It might even be that the external perturbation only plays a minor role in comparison to internal stochastic variations or internal oscillations. This claim is based on several shortcomings in the Milankovitch theory: Prior to one million years ago, the duration of the glacial cycles was indeed 41,000 years, in line with the obliquity cycle of Earth's orbit. This duration changed at the so-called Mid-Pleistocene transition to approximately 100,000 years. Moreover, according to Milankovitch's theory the interglacial of 400,000 years ago should not have happened. Thus, while prior to one million years ago the pacing of these glacial cycles may be tied to changes in Earth's orbit, we do not understand the current magnitude and phasing of the glacial cycles. In principle it is possible that the glacial/interglacial cycles are not due to variations in Earth's orbit, but due to stochastic forcing or internal modes of variability. We present a new method and preliminary results for a unified framework using a fully coupled Earth System Model (ESM), in which the leading three ice age hypotheses will be investigated together. Was the waxing and waning of ice sheets due to an internal mode of variability, due to variations in Earth's orbit, or simply due to a low-order auto-regressive process (i.e., noise integrated by system with memory)? The central idea is to use the Generalized Linear Models (GLM), which can handle both
STABILITY ANALYSIS OF TWO-SECTORS STOCHASTIC ECONOMIC GROWTH MODEL
Institute of Scientific and Technical Information of China (English)
Shaobo ZHOU; Shigeng HU
2007-01-01
In the paper, we investigate the stability of a two-sector economic growth model under stochastic case. A two-dimensional stochastic differential system is deduced by Ito's formula, by using Lyapunov function methods, whether the growth rates of physical capital and human capital are exponentially stable or unstable depends on the values for parameters. Finally, we also illustrate the results with two examples.
Simulation of Stochastic Processes by Coupled ODE-PDE
Zak, Michail
2008-01-01
A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.