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
International Nuclear Information System (INIS)
Granita; Bahar, Arifah
2015-01-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution
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.
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
1962-01-01
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
Deterministic geologic processes and stochastic modeling
International Nuclear Information System (INIS)
Rautman, C.A.; Flint, A.L.
1991-01-01
Recent outcrop sampling at Yucca Mountain, Nevada, has produced significant new information regarding the distribution of physical properties at the site of a potential high-level nuclear waste repository. Consideration of the spatial distribution of measured values and geostatistical measures of spatial variability indicates that there are a number of widespread deterministic geologic features at the site that have important implications for numerical modeling of such performance aspects as ground water flow and radionuclide transport. These deterministic features have their origin in the complex, yet logical, interplay of a number of deterministic geologic processes, including magmatic evolution; volcanic eruption, transport, and emplacement; post-emplacement cooling and alteration; and late-stage (diagenetic) alteration. Because of geologic processes responsible for formation of Yucca Mountain are relatively well understood and operate on a more-or-less regional scale, understanding of these processes can be used in modeling the physical properties and performance of the site. Information reflecting these deterministic geologic processes may be incorporated into the modeling program explicitly, using geostatistical concepts such as soft information, or implicitly, through the adoption of a particular approach to modeling. It is unlikely that any single representation of physical properties at the site will be suitable for all modeling purposes. Instead, the same underlying physical reality will need to be described many times, each in a manner conducive to assessing specific performance issues
Borodin, Andrei N
2017-01-01
This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Stochastic Models in the Identification Process
Czech Academy of Sciences Publication Activity Database
Slovák, Dalibor; Zvárová, Jana
2011-01-01
Roč. 7, č. 1 (2011), s. 44-50 ISSN 1801-5603 R&D Projects: GA MŠk(CZ) 1M06014 Institutional research plan: CEZ:AV0Z10300504 Keywords : identification process * weight-of evidence formula * coancestry coefficient * beta- binomial sampling formula * DNA mixtures Subject RIV: IN - Informatics, Computer Science http://www.ejbi.eu/images/2011-1/Slovak_en.pdf
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.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Energy Technology Data Exchange (ETDEWEB)
Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)
2012-03-15
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
International Nuclear Information System (INIS)
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-01-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-03-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Stochastic growth logistic model with aftereffect for batch fermentation process
International Nuclear Information System (INIS)
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-01-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits
Stochastic growth logistic model with aftereffect for batch fermentation process
Energy Technology Data Exchange (ETDEWEB)
Rosli, Norhayati; Ayoubi, Tawfiqullah [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah; Rahman, Haliza Abdul [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Salleh, Madihah Md [Department of Biotechnology Industry, Faculty of Biosciences and Bioengineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2014-06-19
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
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...
Stochastic process corrosion growth models for pipeline reliability
International Nuclear Information System (INIS)
Bazán, Felipe Alexander Vargas; Beck, André Teófilo
2013-01-01
Highlights: •Novel non-linear stochastic process corrosion growth model is proposed. •Corrosion rate modeled as random Poisson pulses. •Time to corrosion initiation and inherent time-variability properly represented. •Continuous corrosion growth histories obtained. •Model is shown to precisely fit actual corrosion data at two time points. -- Abstract: Linear random variable corrosion models are extensively employed in reliability analysis of pipelines. However, linear models grossly neglect well-known characteristics of the corrosion process. Herein, a non-linear model is proposed, where corrosion rate is represented as a Poisson square wave process. The resulting model represents inherent time-variability of corrosion growth, produces continuous growth and leads to mean growth at less-than-one power of time. Different corrosion models are adjusted to the same set of actual corrosion data for two inspections. The proposed non-linear random process corrosion growth model leads to the best fit to the data, while better representing problem physics
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...
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....
Stochastic processes analysis in nuclear reactor using ARMA models
International Nuclear Information System (INIS)
Zavaljevski, N.
1990-01-01
The analysis of ARMA model derived from general stochastic state equations of nuclear reactor is given. The dependence of ARMA model parameters on the main physical characteristics of RB nuclear reactor in Vinca is presented. Preliminary identification results are presented, observed discrepancies between theory and experiment are explained and the possibilities of identification improvement are anticipated. (author)
Fish Processed Production Planning Using Integer Stochastic Programming Model
Firmansyah, Mawengkang, Herman
2011-06-01
Fish and its processed products are the most affordable source of animal protein in the diet of most people in Indonesia. The goal in production planning is to meet customer demand over a fixed time horizon divided into planning periods by optimizing the trade-off between economic objectives such as production cost and customer satisfaction level. The major decisions are production and inventory levels for each product and the number of workforce in each planning period. In this paper we consider the management of small scale traditional business at North Sumatera Province which performs processing fish into several local seafood products. The inherent uncertainty of data (e.g. demand, fish availability), together with the sequential evolution of data over time leads the production planning problem to a nonlinear mixed-integer stochastic programming model. We use scenario generation based approach and feasible neighborhood search for solving the model. The results which show the amount of each fish processed product and the number of workforce needed in each horizon planning are presented.
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus
2007-01-01
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......, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspondence with the successful description of experiments under low-pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena...
On the modelling of nested risk-neutral stochastic processes with applications in insurance
S.N. Singor (Stefan); A. Boer; J.S.C. Alberts; C.W. Oosterlee (Cornelis)
2017-01-01
textabstractWe propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space
Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process
Turner, Douglas C.; Ladde, Gangaram S.
2018-03-01
Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.
ARMA modelling of neutron stochastic processes with large measurement noise
International Nuclear Information System (INIS)
Zavaljevski, N.; Kostic, Lj.; Pesic, M.
1994-01-01
An autoregressive moving average (ARMA) model of the neutron fluctuations with large measurement noise is derived from langevin stochastic equations and validated using time series data obtained during prompt neutron decay constant measurements at the zero power reactor RB in Vinca. Model parameters are estimated using the maximum likelihood (ML) off-line algorithm and an adaptive pole estimation algorithm based on the recursive prediction error method (RPE). The results show that subcriticality can be determined from real data with high measurement noise using much shorter statistical sample than in standard methods. (author)
Research in Stochastic Processes.
1984-10-01
description, from the stochastic point of view, of the celebrated Hodgkin - Huxley equations. Ph.D. students under Gopinath Kallianpur Victor Perez-Abreu...optimal filter in the general white noise model is shown to be a Markov process. More precisely, it is shown that Ft( Y ) and rt( y ) - the normalized...and unnormalized conditional distribution (where y is the white noise observation) regards as measure-valued processes either on the quasi- P
Stochastic conditional intensity processes
DEFF Research Database (Denmark)
Bauwens, Luc; Hautsch, Nikolaus
2006-01-01
In this article, we introduce the so-called stochastic conditional intensity (SCI) model by extending Russell’s (1999) autoregressive conditional intensity (ACI) model by a latent common dynamic factor that jointly drives the individual intensity components. We show by simulations that the propos...... for a joint latent factor and show that its inclusion allows for an improved and more parsimonious specification of the multivariate intensity process...
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.
International Nuclear Information System (INIS)
Granita; Bahar, A.
2015-01-01
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)
2015-03-09
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.
ARMA modeling of stochastic processes in nuclear reactor with significant detection noise
International Nuclear Information System (INIS)
Zavaljevski, N.
1992-01-01
The theoretical basis of ARMA modelling of stochastic processes in nuclear reactor was presented in a previous paper, neglecting observational noise. The identification of real reactor data indicated that in some experiments the detection noise is significant. Thus a more rigorous theoretical modelling of stochastic processes in nuclear reactor is performed. Starting from the fundamental stochastic differential equations of the Langevin type for the interaction of the detector with neutron field, a new theoretical ARMA model is developed. preliminary identification results confirm the theoretical expectations. (author)
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 ...
Stochastic Models of Evolution
Bezruchko, Boris P.; Smirnov, Dmitry A.
To continue the discussion of randomness given in Sect. 2.2.1, we briefly touch on stochastic models of temporal evolution (random processes). They can be specified either via explicit definition of their statistical properties (probability density functions, correlation functions, etc., Sects. 4.1, 4.2 and 4.3) or via stochastic difference or differential equations. Some of the most widely known equations, their properties and applications are discussed in Sects. 4.4 and 4.5.
Stochastic processes, multiscale modeling, and numerical methods for computational cellular biology
2017-01-01
This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of s...
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 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...... forecasts of the load....
Capasso, Vincenzo
2015-01-01
This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics, and epidemics * Agent-based models New to the Third Edition: * Infinitely divisible distributions * Random measures * Levy processes * Fractional Brownian motion * Ergodic theory * Karhunen-Loeve expansion * Additional applications * Additional exercises * Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Editio...
Stochastic 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.
Using stochastic population process models to predict the impact of climate change.
van der Meer, J.; Beukema, J.J.; Dekker, R.
2013-01-01
More than ten years ago a paper was published in which stochastic population process models were fitted to time series of two marine polychaete species in the western Wadden Sea, The Netherlands (Van der Meer et al., 2000). For the predator species, model fits pointed to a strong effect of average
Levy-Student processes for a stochastic model of beam halos
International Nuclear Information System (INIS)
Petroni, N. Cufaro; De Martino, S.; De Siena, S.; Illuminati, F.
2006-01-01
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 spatiotemporal stochastic process model for species spread.
Fewster, R M
2003-09-01
We use a spatiotemporal Markov process to model the spread of an ecological population through its environment over time. Available habitat is divided into sites, and a parametric function of spatial variables is used to model the probability that one site is colonized from another. This allows us both to make predictions about the future spread of a population, and to determine which are the important factors governing colonizations. The model evolves in discrete time, allowing the population distribution to change seasonally in accordance with breeding patterns. Discrete time formulations are natural for ecological populations, but are problematic due to difficulties of fitting and predicting over irregular time intervals. The model described here can accommodate years of missing data and can therefore fit and predict at irregular intervals. Two methods of approximating the likelihood are described and applied to ornithological survey data for the woodlark, Lullula arborea, from Thetford Forest in the U.K.
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.
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.
Stochastic Analysis of a Queue Length Model Using a Graphics Processing Unit
Czech Academy of Sciences Publication Activity Database
Přikryl, Jan; Kocijan, J.
2012-01-01
Roč. 5, č. 2 (2012), s. 55-62 ISSN 1802-971X R&D Projects: GA MŠk(CZ) MEB091015 Institutional support: RVO:67985556 Keywords : graphics processing unit * GPU * Monte Carlo simulation * computer simulation * modeling Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2012/AS/prikryl-stochastic analysis of a queue length model using a graphics processing unit.pdf
Composite stochastic processes
Kampen, N.G. van
Certain problems in physics and chemistry lead to the definition of a class of stochastic processes. Although they are not Markovian they can be treated explicitly to some extent. In particular, the probability distribution for large times can be found. It is shown to obey a master equation. This
Stochastic Differential Equations and Markov Processes in the Modeling of Electrical Circuits
Directory of Open Access Journals (Sweden)
R. Rezaeyan
2010-06-01
Full Text Available Stochastic differential equations(SDEs, arise from physical systems that possess inherent noise and certainty. We derive a SDE for electrical circuits. In this paper, we will explore the close relationship between the SDE and autoregressive(AR model. We will solve SDE related to RC circuit with using of AR(1 model (Markov process and however with Euler-Maruyama(EM method. Then, we will compare this solutions. Numerical simulations in MATLAB are obtained.
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
Stochastic Modeling and Analysis of Energy Commodity Spot Price Processes
2014-06-27
is a martingale . We shall use this definition to find a risk-neutral dynamics for our model (4.8). Define the riskless asset Bi(t) = exp [∫ t t0 ri... martingale with respect to P̄ , and is given by D1(t) = D10 exp [ −12 ∫ t t0 δ2ds− ∫ t t0 δdW̄1(s) ] D2(t) = D20 exp [ −12 ∫ t t0 σ2(s, y2s − κ1)ds+ ∫ t...Models, Advanced Drug Delivery Reviews, Vol. 65, No. 7, pp 929-939. [34] Doob, J.L., 1955. Martingales and one-dimensional diffusion. Trans. Amer. Math
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...
Model-free stochastic processes studied with q-wavelet-based informational tools
International Nuclear Information System (INIS)
Perez, D.G.; Zunino, L.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.
2007-01-01
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...
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...
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....
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.
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 stochastic model of the processes in PCR based amplification of STR DNA in forensic applications.
Weusten, Jos; Herbergs, Jos
2012-01-01
In forensic DNA profiling use is made of the well-known technique of PCR. When the amount of DNA is high, generally unambiguous profiles can be obtained, but for low copy number DNA stochastic effects can play a major role. In order to shed light on these stochastic effects, we present a simple model for the amplification process. According to the model, three possible things can happen to an individual single DNA strand in each complete cycle: successful amplification, no amplification, or amplification with the introduction of stutter. The model is developed in mathematical terms using a recursive approach: given the numbers of chains at a given cycle, the numbers in the next can be described using a multinomial probability distribution. A full set of recursive relations is derived for the expectations and (co)variances of the number of amplicon chains with no, 1 or 2 stutters. The exact mathematical solutions of this set are given, revealing the development of the expectations and (co)variances as function of the cycle number. The equations reveal that the expected number of amplicon chains without stutter grows exponentially with the cycle number, but for the chains with stutter the relation is more complex. The relative standard deviation on the numbers of chains (coefficient of variation) is inversely proportional to the square root of the expected number of DNA strands entering the amplification. As such, for high copy number DNA the stochastic effects can be ignored, but they play an important role at low concentrations. For the allelic peak, the coefficient of variation rapidly stabilizes after a few cycles, but for the chains with stutter the decrease is more slowly. Further, the ratio of the expected intensity of the stutter peak over that of the allelic peak increases linearly with the number of cycles. Stochastic models, like the one developed in the current paper, can be important in further developing interpretation rules in a Bayesian context
International Nuclear Information System (INIS)
Nafidi, A.; Gutiérrez, R.; Gutiérrez-Sánchez, R.; Ramos-Ábalos, E.; El Hachimi, S.
2016-01-01
The aim of this study is to model electric power consumption during a period of economic crisis, characterised by declining gross domestic product. A novel aspect of this study is its use of a Gamma-type diffusion process for short and medium-term forecasting – other techniques that have been used to describe such consumption patterns are not valid in this situation. In this study, we consider a new extension of the stochastic Gamma diffusion process by introducing time functions (exogenous factors) that affect its trend. This extension is defined in terms of Kolmogorov backward and forward equations. After obtaining the transition probability density function and the moments (specifically, the trend function), the inference on the process parameters is obtained by discrete sampling of the sample paths. Finally, this stochastic process is applied to model total net electricity consumption in Spain, when affected by the following set of exogenous factors: Gross Domestic Product (GDP), Gross Fixed Capital Formation (GFCF) and Final Domestic Consumption (FDC). - Highlights: • The aim is modelling and predicting electricity consumption in Spain. • We propose a Gamma-type diffusion process for short and medium-term forecasting. • We compared the fit using diffusion processes with different exogenous factors.
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Stochastic processes and filtering theory
Jazwinski, Andrew H
1970-01-01
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
Kemper, A; Nishino, T; Schadschneider, A; Zittartz, J
2003-01-01
We develop a new variant of the recently introduced stochastic transfer matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG, adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process are studied and compared with exact data and Monte Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10 sup 5 shows a considerable improvement on the old stochastic TMRG algorithm.
International Nuclear Information System (INIS)
Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William; Bennett, Matthew R.; Josić, Krešimir
2014-01-01
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay
Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Bennett, Matthew R; Josić, Krešimir; Ott, William
2014-05-28
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.
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.
International Nuclear Information System (INIS)
Lee, Kwang Ho; Roh, Myung Sub
2013-01-01
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
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 dynamical model of a growing citation network based on a self-exciting point process.
Golosovsky, Michael; Solomon, Sorin
2012-08-31
We put under experimental scrutiny the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose a citation network of physics papers and traced the citation history of 40,195 papers published in one year. Contrary to common belief, we find that the citation dynamics of the individual papers follows the superlinear preferential attachment, with the exponent α=1.25-1.3. Moreover, we show that the citation process cannot be described as a memoryless Markov chain since there is a substantial correlation between the present and recent citation rates of a paper. Based on our findings we construct a stochastic growth model of the citation network, perform numerical simulations based on this model and achieve an excellent agreement with the measured citation distributions.
Cushman, John H.
1987-04-01
In a recent review article, G. Sposito et al. (1986) examined the various stochastic theories which are concerned with transport of solutes in porous media. In this short note we expand on their discussion to include several topics which had been omitted. We begin by looking at two definitions of probability theory and their relation to the concept of an ensemble. An REV ensemble of soils is defined and examined. The concept of ergodicity is reviewed, and it is pointed out that most stochastic models are theoretically unverifiable. The relationship between scale of measurement and stochasticity is briefly reviewed, and an equation that combines the two concepts is presented.
Measure of Uncertainty in Process Models Using Stochastic Petri Nets and Shannon Entropy
Directory of Open Access Journals (Sweden)
Martin Ibl
2016-01-01
Full Text Available When modelling and analysing business processes, the main emphasis is usually put on model validity and accuracy, i.e., the model meets the formal specification and also models the relevant system. In recent years, a series of metrics has begun to develop, which allows the quantification of the specific properties of process models. These characteristics are, for instance, complexity, comprehensibility, cohesion, and uncertainty. This work is focused on defining a method that allows us to measure the uncertainty of a process model, which was modelled by using stochastic Petri nets (SPN. The principle of this method consists of mapping of all reachable marking of SPN into the continuous-time Markov chain and then calculating its stationary probabilities. The uncertainty is then measured as the entropy of the Markov chain (it is possible to calculate the uncertainty of the specific subset of places as well as of whole net. Alternatively, the uncertainty index is quantified as a percentage of the calculated entropy against maximum entropy (the resulting value is normalized to the interval <0,1>. The calculated entropy can also be used as a measure of the model complexity.
Stochastic Greybox Modeling for Control of an Alternating Activated Sludge Process
DEFF Research Database (Denmark)
Halvgaard, Rasmus Fogtmann; Vezzaro, Luca; Grum, M.
We present a stochastic greybox model of a BioDenitro WWTP that can be used for short time horizon Model Predictive Control. The model is based on a simpliﬁed ASM1 model and takes model uncertainty in to account. It estimates unmeasured state variables in the system, e.g. the inlet concentration...
Stochastic processes, slaves and supersymmetry
International Nuclear Information System (INIS)
Drummond, I T; Horgan, R R
2012-01-01
We extend the work of Tănase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We consider both the stochastic differential equations (SDEs) for the process and the associated diffusion equation. The influence of the disturbances can be understood by augmenting the original SDE with an equation for slave variables. The evolution of the slave variables describes the behaviour of line elements carried along in the stochastic flow. These line elements, together with the associated surface and volume elements constructed from them, provide the basis of the supersymmetry properties of the theory. For ease of visualization, and in order to emphasize a helpful electromagnetic analogy, we work in three dimensions. The results are all generalizable to higher dimensions and can be specialized to one and two dimensions. The electromagnetic analogy is a useful starting point for calculating asymptotic results at low temperature that can be compared with direct numerical evaluations. We also examine the problems that arise in a direct numerical simulation of the stochastic equation together with the slave equations. We pay special attention to the dependence of the slave variable statistics on temperature. We identify in specific models the critical temperature below which the slave variable distribution ceases to have a variance and consider the effect on estimates of susceptibilities. (paper)
Tucker, C. J.; Garratt, M. W.
1977-01-01
A stochastic leaf radiation model based upon physical and physiological properties of dicot leaves has been developed. The model accurately predicts the absorbed, reflected, and transmitted radiation of normal incidence as a function of wavelength resulting from the leaf-irradiance interaction over the spectral interval of 0.40-2.50 micron. The leaf optical system has been represented as Markov process with a unique transition matrix at each 0.01-micron increment between 0.40 micron and 2.50 micron. Probabilities are calculated at every wavelength interval from leaf thickness, structure, pigment composition, and water content. Simulation results indicate that this approach gives accurate estimations of actual measured values for dicot leaf absorption, reflection, and transmission as a function of wavelength.
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
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.
Sedwards, Sean; Mazza, Tommaso
2007-10-15
Compartments and membranes are the basis of cell topology and more than 30% of the human genome codes for membrane proteins. While it is possible to represent compartments and membrane proteins in a nominal way with many mathematical formalisms used in systems biology, few, if any, explicitly model the topology of the membranes themselves. Discrete stochastic simulation potentially offers the most accurate representation of cell dynamics. Since the details of every molecular interaction in a pathway are often not known, the relationship between chemical species in not necessarily best described at the lowest level, i.e. by mass action. Simulation is a form of computer-aided analysis, relying on human interpretation to derive meaning. To improve efficiency and gain meaning in an automatic way, it is necessary to have a formalism based on a model which has decidable properties. We present Cyto-Sim, a stochastic simulator of membrane-enclosed hierarchies of biochemical processes, where the membranes comprise an inner, outer and integral layer. The underlying model is based on formal language theory and has been shown to have decidable properties (Cavaliere and Sedwards, 2006), allowing formal analysis in addition to simulation. The simulator provides variable levels of abstraction via arbitrary chemical kinetics which link to ordinary differential equations. In addition to its compact native syntax, Cyto-Sim currently supports models described as Petri nets, can import all versions of SBML and can export SBML and MATLAB m-files. Cyto-Sim is available free, either as an applet or a stand-alone Java program via the web page (http://www.cosbi.eu/Rpty_Soft_CytoSim.php). Other versions can be made available upon request.
Lopopolo, Alessandro; Frank, Stefan L; van den Bosch, Antal; Willems, Roel M
2017-01-01
Language comprehension involves the simultaneous processing of information at the phonological, syntactic, and lexical level. We track these three distinct streams of information in the brain by using stochastic measures derived from computational language models to detect neural correlates of phoneme, part-of-speech, and word processing in an fMRI experiment. Probabilistic language models have proven to be useful tools for studying how language is processed as a sequence of symbols unfolding in time. Conditional probabilities between sequences of words are at the basis of probabilistic measures such as surprisal and perplexity which have been successfully used as predictors of several behavioural and neural correlates of sentence processing. Here we computed perplexity from sequences of words and their parts of speech, and their phonemic transcriptions. Brain activity time-locked to each word is regressed on the three model-derived measures. We observe that the brain keeps track of the statistical structure of lexical, syntactic and phonological information in distinct areas.
Space-time-modulated stochastic processes.
Giona, Massimiliano
2017-10-01
Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.
Space-time-modulated stochastic processes
Giona, Massimiliano
2017-10-01
Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.
Stochastic 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...
Analytic Hierarchy Process (AHP in Ranking Non-Parametric Stochastic Rainfall and Streamflow Models
Directory of Open Access Journals (Sweden)
Masengo Ilunga
2015-08-01
Full Text Available Analytic Hierarchy Process (AHP is used in the selection of categories of non-parametric stochastic models for hydrological data generation and its formulation is based on pairwise comparisons of models. These models or techniques are obtained from a recent study initiated by the Water Research Commission of South Africa (WRC and were compared predominantly based on their capability to extrapolate data beyond the range of historic hydrological data. The different categories of models involved in the selection process were: wavelet (A, reordering (B, K-nearest neighbor (C, kernel density (D and bootstrap (E. In the AHP formulation, criteria for the selection of techniques are: "ability for data to preserve historic characteristics", "ability to generate new hydrological data", "scope of applicability", "presence of negative data generated" and "user friendliness". The pairwise comparisons performed through AHP showed that the overall order of selection (ranking of models was D, C, A, B and C. The weights of these techniques were found to be 27.21%, 24.3 %, 22.15 %, 13.89 % and 11.80 % respectively. Hence, bootstrap category received the highest preference while nearest neighbor received the lowest preference when all selection criteria are taken into consideration.
Stochastic model in microwave propagation
International Nuclear Information System (INIS)
Ranfagni, A.; Mugnai, D.
2011-01-01
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.
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...
International Nuclear Information System (INIS)
Zwingelstein, Gilles; Thabet, Gabriel.
1977-01-01
Control algorithms for components of nuclear power plants are currently based on external diagnostic methods. Modeling and identification techniques for autoregressive moving average models (ARMA) for stochastic processes are described. The identified models provide a means of estimating the power spectral density with improved accuracy and computer time compared with the classical methods. They are particularly will suited for on-line estimation of the power spectral density. The observable stochastic process y (t) is modeled assuming that it is the output of a linear filter driven by Gaussian while noise w (t). Two identification schemes were tested to find the orders m and n of the ARMA (m,n) models and to estimate the parameters of the recursion equation relating the input and output signals. The first scheme consists in transforming the ARMA model to an autoregressive model. The parameters of this AR model are obtained using least squares estimation techniques. The second scheme consists in finding the parameters of the ARMA by nonlinear programming techniques. The power spectral density of y(t) is instantaneously deduced from these ARMA models [fr
Statistical inference for stochastic processes
National Research Council Canada - National Science Library
Basawa, Ishwar V; Prakasa Rao, B. L. S
1980-01-01
The aim of this monograph is to attempt to reduce the gap between theory and applications in the area of stochastic modelling, by directing the interest of future researchers to the inference aspects...
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.
Anomalous transport and stochastic processes
Energy Technology Data Exchange (ETDEWEB)
Balescu, R. [Universite Libre de Bruxelles (Belgium)
1996-03-01
The relation between kinetic transport theory and theory of stochastic processes is reviewed. The Langevin equation formalism provides important, but rather limited information about diffusive processes. A quite promising new approach to modeling complex situations, such as transport in incompletely destroyed magnetic surfaces, is provided by the theory of Continuous Time Random Walks (CTRW), which is presented in some detail. An academic test problem is discussed in great detail: transport of particles in a fluctuating magnetic field, in the limit of infinite perpendicular correlation length. The well-known subdiffusive behavior of the Mean Square Displacement (MSD), proportional to t{sup 1/2}, is recovered by a CTRW, but the complete density profile is not. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW. 16 refs., 3 figs.
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...
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.
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.
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...... to the Bichteler-Dellacherie Theorem. The semimartingale property of Gaussian processes is characterized in terms of their covariance function, spectral measure and spectral representation. In addition, representation and expansion of filtration results are provided as well. Special attention is given to moving...
Verification of Stochastic Process Calculi
DEFF Research Database (Denmark)
Skrypnyuk, Nataliya
process calculi. The description of a system in the syntax of a particular stochastic process calculus can be analysed in a compositional way, without expanding the state space by explicitly resolving all the interdependencies between the subsystems which may lead to the state space explosion problem....... In support of this claim we have developed analysis methods that belong to a particular type of Static Analysis { Data Flow / Pathway Analysis. These methods have previously been applied to a number of non-stochastic process calculi. In this thesis we are lifting them to the stochastic calculus...... description of a system. The presented methods have a clear application in the areas of embedded systems, (randomised) protocols run between a fixed number of parties etc....
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.
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
Stochastic modeling of catalytic processes in nanoporous materials: Beyond mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Garcia, Andres [Iowa State Univ., Ames, IA (United States)
2017-08-05
Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems can be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use
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.
Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P
2008-01-01
Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...
Stochastic 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.
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.
Is human failure a stochastic process?
International Nuclear Information System (INIS)
Dougherty, Ed M.
1997-01-01
Human performance results in failure events that occur with a risk-significant frequency. System analysts have taken for granted the random (stochastic) nature of these events in engineering assessments such as risk assessment. However, cognitive scientists and error technologists, at least those who have interest in human reliability, have, over the recent years, claimed that human error does not need this stochastic framework. Yet they still use the language appropriate to stochastic processes. This paper examines the potential for the stochastic nature of human failure production as the basis for human reliability analysis. It distinguishes and leaves to others, however, the epistemic uncertainties over the possible probability models for the real variability of human performance
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.
Stochastic modelling of landfill processes incorporating waste heterogeneity and data uncertainty
International Nuclear Information System (INIS)
Zacharof, A.I.; Butler, A.P.
2004-01-01
A landfill is a very complex heterogeneous environment and as such it presents many modelling challenges. Attempts to develop models that reproduce these complexities generally involve the use of large numbers of spatially dependent parameters that cannot be properly characterised in the face of data uncertainty. An alternative method is presented, which couples a simplified microbial degradation model with a stochastic hydrological and contaminant transport model. This provides a framework for incorporating the complex effects of spatial heterogeneity within the landfill in a simplified manner, along with other key variables. A methodology for handling data uncertainty is also integrated into the model structure. Illustrative examples of the model's output are presented to demonstrate effects of data uncertainty on leachate composition and gas volume prediction
Stochastic Models of Soil Denitrification
Parkin, T. B.; Robinson, J. A.
1989-01-01
Soil denitrification is a highly variable process that appears to be lognormally distributed. This variability is manifested by large sample coefficients of variation for replicate estimates of soil core denitrification rates. Deterministic models for soil denitrification have been proposed in the past, but none of these models predicts the approximate lognormality exhibited by natural denitrification rate estimates. In this study, probabilistic (stochastic) models were developed to understand how positively skewed distributions for field denitrification rate estimates result from the combined influences of variables known to affect denitrification. Three stochastic models were developed to describe the distribution of measured soil core denitrification rates. The driving variables used for all the models were denitrification enzyme activity and CO2 production rates. The three models were distinguished by the functional relationships combining these driving variables. The functional relationships used were (i) a second-order model (model 1), (ii) a second-order model with a threshold (model 2), and (iii) a second-order saturation model (model 3). The parameters of the models were estimated by using 12 separate data sets (24 replicates per set), and their abilities to predict denitrification rate distributions were evaluated by using three additional independent data sets of 180 replicates each. Model 2 was the best because it produced distributions of denitrification rate which were not significantly different (P > 0.1) from distributions of measured denitrification rates. The generality of this model is unknown, but it accurately predicted the mean denitrification rates and accounted for the stochastic nature of this variable at the site studied. The approach used in this study may be applicable to other areas of ecological research in which accounting for the high spatial variability of microbiological processes is of interest. PMID:16347838
Introduction to stochastic processes
Cinlar, Erhan
2013-01-01
Clear presentation employs methods that recognize computer-related aspects of theory. Topics include expectations and independence, Bernoulli processes and sums of independent random variables, Markov chains, renewal theory, more. 1975 edition.
Temperature stochastic modeling and weather derivatives pricing ...
African Journals Online (AJOL)
... over a sufficient period to apply a stochastic process that describes the evolution of the temperature. A numerical example of a swap contract pricing is presented, using an approximation formula as well as Monte Carlo simulations. Keywords: Weather derivatives, temperature stochastic model, Monte Carlo simulation.
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.
Esparza, Javier
In many areas of computer science entities can “reproduce”, “replicate”, or “create new instances”. Paramount examples are threads in multithreaded programs, processes in operating systems, and computer viruses, but many others exist: procedure calls create new incarnations of the callees, web crawlers discover new pages to be explored (and so “create” new tasks), divide-and-conquer procedures split a problem into subproblems, and leaves of tree-based data structures become internal nodes with children. For lack of a better name, I use the generic term systems with process creation to refer to all these entities.
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
Dynamical and hamiltonian dilations of stochastic processes
International Nuclear Information System (INIS)
Baumgartner, B.; Gruemm, H.-R.
1982-01-01
This is a study of the problem, which stochastic processes could arise from dynamical systems by loss of information. The notions of ''dilation'' and ''approximate dilation'' of a stochastic process are introduced to give exact definitions of this particular relationship. It is shown that every generalized stochastic process is approximately dilatable by a sequence of dynamical systems, but for stochastic processes in full generality one needs nets. (Author)
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
Stochastic Models of Human Errors
Elshamy, Maged; Elliott, Dawn M. (Technical Monitor)
2002-01-01
Humans play an important role in the overall reliability of engineering systems. More often accidents and systems failure are traced to human errors. Therefore, in order to have meaningful system risk analysis, the reliability of the human element must be taken into consideration. Describing the human error process by mathematical models is a key to analyzing contributing factors. Therefore, the objective of this research effort is to establish stochastic models substantiated by sound theoretic foundation to address the occurrence of human errors in the processing of the space shuttle.
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
2017-02-01
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 C q = 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.
Streamer inception from hydrometeors as a stochastic process with a particle-based model
Rutjes, Casper; Dubinova, Anna; Ebert, Ute; Teunissen, Jannis; Buitink, Stijn; Scholten, Olaf; Trihn, Gia
2017-04-01
In thunderstorms, streamers (as precursors for lightning leaders) 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 shower 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. Therefore, we developed a new stochastic particle-based model to study the behavior of the system described above, to calculate the probability of streamer inception, for given hydrometeor, electric field and initial electron density. Results show that the discharge starts with great jitter and usually off the symmetry axis, demanding stochastic approach in full 3D for streamer inception in realistic thunderstorm conditions. The developed software will be made publically available as an open source project. [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.
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.
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...
Dias, Edgard; Ebdon, James; Taylor, Huw
2015-01-01
This study proposes that calculating and interpreting removal coefficients (K20) for bacteriophages in activated sludge (AS) and trickling filter (TF) systems using stochastic modelling may provide important information that may be used to estimate the removal of phages in such systems using simplified models. In order to achieve this, 14 samples of settled wastewater and post-secondary sedimentation wastewater were collected every 2 weeks, over a 6-month period (May to November), from two AS and two TF systems situated in southern England. Initial results have demonstrated that the removal of somatic coliphages in both AS and TF systems is considerably higher than that of F-RNA coliphages, and that AS more effectively removes both phage groups than TF. The results have also demonstrated that K20 values for phages in AS are higher than in TF, which could be justified by the higher removal rates observed in AS and the models assumed for both systems. The research provides a suggested framework for calculating and predicting removal rates of pathogens and indicator organisms in wastewater treatment systems using simplified models in order to support integrated water and sanitation safety planning approaches to human health risk management.
A stochastic model for the financial market with discontinuous prices
Directory of Open Access Journals (Sweden)
Leda D. Minkova
1996-01-01
Full Text Available This paper models some situations occurring in the financial market. The asset prices evolve according to a stochastic integral equation driven by a Gaussian martingale. A portfolio process is constrained in such a way that the wealth process covers some obligation. A solution to a linear stochastic integral equation is obtained in a class of cadlag stochastic processes.
Modeling bias and variation in the stochastic processes of small RNA sequencing.
Argyropoulos, Christos; Etheridge, Alton; Sakhanenko, Nikita; Galas, David
2017-06-20
The use of RNA-seq as the preferred method for the discovery and validation of small RNA biomarkers has been hindered by high quantitative variability and biased sequence counts. In this paper we develop a statistical model for sequence counts that accounts for ligase bias and stochastic variation in sequence counts. This model implies a linear quadratic relation between the mean and variance of sequence counts. Using a large number of sequencing datasets, we demonstrate how one can use the generalized additive models for location, scale and shape (GAMLSS) distributional regression framework to calculate and apply empirical correction factors for ligase bias. Bias correction could remove more than 40% of the bias for miRNAs. Empirical bias correction factors appear to be nearly constant over at least one and up to four orders of magnitude of total RNA input and independent of sample composition. Using synthetic mixes of known composition, we show that the GAMLSS approach can analyze differential expression with greater accuracy, higher sensitivity and specificity than six existing algorithms (DESeq2, edgeR, EBSeq, limma, DSS, voom) for the analysis of small RNA-seq data. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.
Statistical validation of stochastic models
Energy Technology Data Exchange (ETDEWEB)
Hunter, N.F. [Los Alamos National Lab., NM (United States). Engineering Science and Analysis Div.; Barney, P.; Paez, T.L. [Sandia National Labs., Albuquerque, NM (United States). Experimental Structural Dynamics Dept.; Ferregut, C.; Perez, L. [Univ. of Texas, El Paso, TX (United States). Dept. of Civil Engineering
1996-12-31
It is common practice in structural dynamics to develop mathematical models for system behavior, and the authors are now capable of developing stochastic models, i.e., models whose parameters are random variables. Such models have random characteristics that are meant to simulate the randomness in characteristics of experimentally observed systems. This paper suggests a formal statistical procedure for the validation of mathematical models of stochastic systems when data taken during operation of the stochastic system are available. The statistical characteristics of the experimental system are obtained using the bootstrap, a technique for the statistical analysis of non-Gaussian data. The authors propose a procedure to determine whether or not a mathematical model is an acceptable model of a stochastic system with regard to user-specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.
Stochastic Subspace Modelling of Turbulence
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
2009-01-01
positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order......, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.......Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper...
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.
Discrete stochastic processes and applications
Collet, Jean-François
2018-01-01
This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy.
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...
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......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...... to define, analyze, and compare most channel models already suggested in literature and that the powerful tools of this framework have not been fully exploited in this context yet....
Stochastic models of technology diffusion
Energy Technology Data Exchange (ETDEWEB)
Horner, S.M.
1978-01-01
Simple stochastic models of epidemics have often been employed by economists and sociologists in the study of the diffusion of information or new technology. In the present theoretical inquiry the properties of a family of models related to these epidemic processes are investigated, and use of the results in the study of technical change phenomena is demonstrated. A moving limit to the level of productivity of capital is hypothesized, the exact increment is determined exogenously by basic or applied research carried on outside the industry. It is this level of latent productivity (LPRO) which fills the role of the ''disease'' which ''spreads'' through the industry. In the single advance models, LPRO is assumed to have moved forward at some point in time, after which an individual firm may advance to the limit by virtue of its own research and development or through imitation of the successful efforts of another firm. In the recurrent advance models, LPRO is assumed to increase at either a constant absolute or relative rate. The firms, in the course of their research and imitation efforts, follow behind LPRO. Using the methods of stochastic processes, it is shown that these models are equivalent to ergodic Markov chains. Based on an assumption of constant intensity of R and D effort, it is shown how the single and recurrent advance models reflect on Joseph Schumpeter's hypothesis that more concentrated industries tend to be more technologically advanced than less concentrated. The results corroborate the weakest version of the hypothesis: monopoly prices need not be higher than competitive prices.
spate: An R Package for Spatio-Temporal Modeling with a Stochastic Advection-Diffusion Process
Directory of Open Access Journals (Sweden)
Fabio Sigrist
2015-02-01
This package aims at providing tools for simulating and modeling of spatio-temporal processes using an SPDE based approach. The package contains functions for obtaining parametrizations, such as propagator or innovation covariance matrices, of the spatio-temporal model. This allows for building customized hierarchical Bayesian models using the SPDE based model at the process stage. The functions of the package then provide computationally efficient algorithms needed for doing inference with the hierarchical model. Furthermore, an adaptive Markov chain Monte Carlo (MCMC algorithm implemented in the package can be used as an algorithm for doing inference without any additional modeling. This function is flexible and allows for application specific customizing. The MCMC algorithm supports data that follow a Gaussian or a censored distribution with point mass at zero. Spatio-temporal covariates can be included in the model through a regression term.
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.
Multiplier Models in Stochastic DEA
Directory of Open Access Journals (Sweden)
Mahnaz Mirbolouki
2014-05-01
Full Text Available Data Envelopment Analysis (DEA is a data-oriented performance evaluation method which has treated data as being deterministic. Throughout applications managers may encounter the data which are not recognized deterministically. In this paper a deterministic version of stochastic CCR multiplier model based on chance constrained programming approach is presented. The advantage of this method is that the stochastic essence of input-output variables has been taken into account. Using numerical example, we will demonstrate how this method works.
Counseling as a Stochastic Process: Fitting a Markov Chain Model to Initial Counseling Interviews
Lichtenberg, James W.; Hummel, Thomas J.
1976-01-01
The goodness of fit of a first-order Markov chain model to six counseling interviews was assessed by using chi-square tests of homogeneity and simulating sampling distributions of selected process characteristics against which the same characteristics in the actual interviews were compared. The model fit four of the interviews. Presented at AERA,…
Papalexiou, Simon Michael
2018-05-01
Hydroclimatic processes come in all "shapes and sizes". They are characterized by different spatiotemporal correlation structures and probability distributions that can be continuous, mixed-type, discrete or even binary. Simulating such processes by reproducing precisely their marginal distribution and linear correlation structure, including features like intermittency, can greatly improve hydrological analysis and design. Traditionally, modelling schemes are case specific and typically attempt to preserve few statistical moments providing inadequate and potentially risky distribution approximations. Here, a single framework is proposed that unifies, extends, and improves a general-purpose modelling strategy, based on the assumption that any process can emerge by transforming a specific "parent" Gaussian process. A novel mathematical representation of this scheme, introducing parametric correlation transformation functions, enables straightforward estimation of the parent-Gaussian process yielding the target process after the marginal back transformation, while it provides a general description that supersedes previous specific parameterizations, offering a simple, fast and efficient simulation procedure for every stationary process at any spatiotemporal scale. This framework, also applicable for cyclostationary and multivariate modelling, is augmented with flexible parametric correlation structures that parsimoniously describe observed correlations. Real-world simulations of various hydroclimatic processes with different correlation structures and marginals, such as precipitation, river discharge, wind speed, humidity, extreme events per year, etc., as well as a multivariate example, highlight the flexibility, advantages, and complete generality of the method.
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.
Stochastic Wake Modelling Based on POD Analysis
Directory of Open Access Journals (Sweden)
David Bastine
2018-03-01
Full Text Available In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD, three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained.
Joseph Buongiorno
2001-01-01
Faustmann's formula gives the land value, or the forest value of land with trees, under deterministic assumptions regarding future stand growth and prices, over an infinite horizon. Markov decision process (MDP) models generalize Faustmann's approach by recognizing that future stand states and prices are known only as probabilistic distributions. The...
100 years after Smoluchowski: stochastic processes in cell biology
International Nuclear Information System (INIS)
Holcman, D; Schuss, Z
2017-01-01
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. (topical review)
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.
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. Copyright © 2015 John Wiley & Sons, Ltd.
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...
Weather Derivatives and Stochastic Modelling of Temperature
Directory of Open Access Journals (Sweden)
Fred Espen Benth
2011-01-01
Full Text Available We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.
Stochastic 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.
Birch regeneration: a stochastic model
William B. Leak
1968-01-01
The regeneration of a clearcutting with paper or yellow birch is expressed as an elementary stochastic (probabalistic) model that is computationally similar to an absorbing Markov chain. In the general case, the model contains 29 states beginning with the development of a flower (ament) and terminating with the abortion of a flower or seed, or the development of an...
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
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 modeling of soil salinity
Suweis, S.; Porporato, A. M.; Daly, E.; van der Zee, S.; Maritan, A.; Rinaldo, A.
2010-12-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The equations for the probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equations to a single stochastic differential equation (generalized Langevin equation) driven by multiplicative Poisson noise. Generalized Langevin equations with multiplicative white Poisson noise pose the usual Ito (I) or Stratonovich (S) prescription dilemma. Different interpretations lead to different results and then choosing between the I and S prescriptions is crucial to describe correctly the dynamics of the model systems. We show how this choice can be determined by physical information about the timescales involved in the process. We also show that when the multiplicative noise is at most linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We then apply these results to the generalized Langevin equation that drives the salt mass dynamics. The stationary analytical solutions for the probability density functions of salt mass and concentration provide insight on the interplay of the main soil, plant and climate parameters responsible for long term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in longterm soil salinization trends, with significant consequences, e.g. for climate change impacts on rain fed agriculture.
Stochastic 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...... are described, as at the time of publication these methods represent new contribution to hydrology. The second part also contains additional description of software used and a brief introduction to stiff systems. The system in one of the papers is stiff....
Stochastic hyperelastic modeling considering dependency of material parameters
Caylak, Ismail; Penner, Eduard; Dridger, Alex; Mahnken, Rolf
2018-03-01
This paper investigates the uncertainty of a hyperelastic model by treating random material parameters as stochastic variables. For its stochastic discretization a polynomial chaos expansion (PCE) is used. An important aspect in our work is the consideration of stochastic dependencies in the stochastic modeling of Ogden's material model. To this end, artificial experiments are generated using the auto-regressive moving average process based on real experiments. The parameter identification for all data provides statistics of Ogden's material parameters, which are subsequently used for stochastic modeling. Stochastic dependencies are incorporated into the PCE using a Nataf transformation from dependent distributed random variables to independent standard normal distributed ones. The representative numerical example shows that our proposed method adequately takes into account the stochastic dependencies of Ogden's material parameters.
Stochastic modeling of soil salinity
Suweis, S.; Rinaldo, A.; Zee, van der S.E.A.T.M.; Daly, E.; Maritan, A.
2010-01-01
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
Stochastic Growth Models with No Discounting
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2007-01-01
Roč. 15, č. 4 (2007), s. 88-98 ISSN 0572-3043 R&D Projects: GA ČR(CZ) GA402/06/0990; GA ČR GA402/05/0115 Institutional research plan: CEZ:AV0Z10750506 Keywords : economic dynamics * stochastic version of the Ramsey growth model * Markov decision processes Subject RIV: AH - Economics
Stochastic models for road traffic control
Kovács, P.
2016-01-01
In this dissertation we make use of the theories of stochastic processes and operations research to develop models and methods to be applied for the analysis and control of road traffic networks. Within this field three subjects are considered: individual routing, urban traffic light networks and
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 stochastic modeling of recurrent measles epidemic | Kassem ...
African Journals Online (AJOL)
A simple stochastic mathematical model is developed and investigated for the dynamics of measles epidemic. The model, which is a multi-dimensional diffusion process, includes susceptible individuals, latent (exposed), infected and removed individuals. Stochastic effects are assumed to arise in the process of infection of ...
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
A Stochastic Model for Malaria Transmission Dynamics
Directory of Open Access Journals (Sweden)
Rachel Waema Mbogo
2018-01-01
Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.
Stochastic and deterministic trend models
Estela Bee Dagum; Camilo Dagum
2008-01-01
In this paper we provide an overview of some trend models formulated for global and local estimation. Global trend models are based on the assumption that the trend or nonstationary mean of a time series can be approximated closely by simple functions of time over the entire span of the series. The most common representation of deterministic and stochastic trend are introduced. In particular, for the former we analyze polynomial and transcendental functions, whereas for the latter we assume t...
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
International Nuclear Information System (INIS)
Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng
2008-01-01
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies
Hopf bifurcation of the stochastic model on business cycle
International Nuclear Information System (INIS)
Xu, J; Wang, H; Ge, G
2008-01-01
A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Stochastic 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.
Probability and stochastic modeling
Rotar, Vladimir I
2012-01-01
Basic NotionsSample Space and EventsProbabilitiesCounting TechniquesIndependence and Conditional ProbabilityIndependenceConditioningThe Borel-Cantelli TheoremDiscrete Random VariablesRandom Variables and VectorsExpected ValueVariance and Other Moments. Inequalities for DeviationsSome Basic DistributionsConvergence of Random Variables. The Law of Large NumbersConditional ExpectationGenerating Functions. Branching Processes. Random Walk RevisitedBranching Processes Generating Functions Branching Processes Revisited More on Random WalkMarkov ChainsDefinitions and Examples. Probability Distributions of Markov ChainsThe First Step Analysis. Passage TimesVariables Defined on a Markov ChainErgodicity and Stationary DistributionsA Classification of States and ErgodicityContinuous Random VariablesContinuous DistributionsSome Basic Distributions Continuous Multivariate Distributions Sums of Independent Random Variables Conditional Distributions and ExpectationsDistributions in the General Case. SimulationDistribution F...
CircE: an R implementation of Browne's circular stochastic process model.
Grassi, Michele; Luccio, Riccardo; Di Blas, Lisa
2010-02-01
In confirmatory analysis of whether data have a circumplex structure, Browne's (1992) model has played a major role. However, implementation of this model requires a dedicated program, CIRCUM, because the analysis routine is not integrated in any of the most widely used statistical software packages. Hence, data entry and graphical representation of the results require the use of one or more additional programs. We propose a package for the R statistical environment, termed CircE, that can be used to enter or import data, implement Browne's confirmatory analysis, and graphically represent the results. Using this new software, we put forward a new approach to assess the sustainability of theoretical models when the analysis is carried out at the level of questionnaire items. The CircE package (for either Mac OS X or Windows) and additional files may be downloaded from http://brm.psychonomic-journals.org/content/supplemental.
Stochastic Models for Carcinogenesis
1961-01-01
Court Brown and Doll [3] on patients irradiated for ankylosing spondylitis . In their data, however, the peak incidence of leukemia occurred as soon as...and AploAtic Anaemia in Patients Irra- diated for Ankylosing Spondylitis , Special Report Series, Medical Research Council, No. 295, London, Her...function D(u). The possibilities are, of course, wide, and we shall not attempt any general treatment of such a model, although some particular cases will be
Stochastic Still Water Response Model
DEFF Research Database (Denmark)
Friis-Hansen, Peter; Ditlevsen, Ove Dalager
2002-01-01
water bending moment is compared to statistics from available regression formulas. It is found that the suggested model predicts a coefficient of variation of the maximum still water bending moment that is a factor of two to three times lower than that obtained by use of the regression formula. It turns......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...
American option pricing with stochastic volatility processes
Directory of Open Access Journals (Sweden)
Ping LI
2017-12-01
Full Text Available In order to solve the problem of option pricing more perfectly, the option pricing problem with Heston stochastic volatility model is considered. The optimal implementation boundary of American option and the conditions for its early execution are analyzed and discussed. In view of the fact that there is no analytical American option pricing formula, through the space discretization parameters, the stochastic partial differential equation satisfied by American options with Heston stochastic volatility is transformed into the corresponding differential equations, and then using high order compact finite difference method, numerical solutions are obtained for the option price. The numerical experiments are carried out to verify the theoretical results and simulation. The two kinds of optimal exercise boundaries under the conditions of the constant volatility and the stochastic volatility are compared, and the results show that the optimal exercise boundary also has stochastic volatility. Under the setting of parameters, the behavior and the nature of volatility are analyzed, the volatility curve is simulated, the calculation results of high order compact difference method are compared, and the numerical option solution is obtained, so that the method is verified. The research result provides reference for solving the problems of option pricing under stochastic volatility such as multiple underlying asset option pricing and barrier option pricing.
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...
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.
Minimum Entropy Rate Simplification of Stochastic Processes.
Henter, Gustav Eje; Kleijn, W Bastiaan
2016-02-23
This document contains supplemental material for the IEEE Transactions on Pattern Analysis and Machine Intelligence article "Minimum Entropy Rate Simplification of Stochastic Processes." The supplement is divided into three appen- dices: the first on MERS for Gaussian processes, and the remaining two on, respectively, the theory and the experimental results of MERS for Markov chains.
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 models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Sequential neural models with stochastic layers
DEFF Research Database (Denmark)
Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich
2016-01-01
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...
ON REGRESSION REPRESENTATIONS OF STOCHASTIC-PROCESSES
RUSCHENDORF, L; DEVALK, [No Value
We construct a.s. nonlinear regression representations of general stochastic processes (X(n))n is-an-element-of N. As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive
Stochastic models for cell division
Stukalin, Evgeny; Sun, Sean
2013-03-01
The probability of cell division per unit time strongly depends of age of cells, i.e., time elapsed since their birth. The theory of cell populations in the age-time representation is systematically applied for modeling cell division for different spreads in generation times. We use stochastic simulations to address the same issue at the level of individual cells. Our approach unlike deterministic theory enables to analyze the size fluctuations of cell colonies at different growth conditions (in the absence and in the presence of cell death, for initially synchronized and asynchronous cell populations, for conditions of restricted growth). We find the simple quantitative relation between the asymptotic values of relative size fluctuations around mean values for initially synchronized cell populations under growth and the coefficients of variation of generation times. Effect of initial age distribution for asynchronous growth of cell cultures is also studied by simulations. The influence of constant cell death on fluctuations of sizes of cell populations is found to be essential even for small cell death rates, i.e., for realistic growth conditions. The stochastic model is generalized for biologically relevant case that involves both cell reproduction and cell differentiation.
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...
Stationary stochastic processes theory and applications
Lindgren, Georg
2012-01-01
Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued stochastic processesBochner's theorem and the spectral distributionSpectral representation of a stationary processGaussian processesStationary counting processesExercisesLinear Filters - General PropertiesLinear time invariant filtersLinear filters and differential equationsWhite noise in linear systemsLong range dependence, non-integrable spectra, and unstable systemsThe ARMA-familyLinear Filters - Special TopicsThe Hilbert transform and the envelopeThe sampling theoremKarhunen-Loève expansionClassical Ergodic Theory and MixingThe basic ergodic theorem in L2Stationarity and transformationsThe ergodic th...
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...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Stochastic hyperfine interactions modeling library
Zacate, Matthew O.; Evenson, William E.
2011-04-01
The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When
Modelling Evolutionary Algorithms with Stochastic Differential Equations.
Heredia, Jorge Pérez
2017-11-20
There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.
Logics and Models for Stochastic Analysis Beyond Markov Chains
DEFF Research Database (Denmark)
Zeng, Kebin
form of discrete PH distributions as computational vehicle on measuring the performance of concurrent wireless sensor networks. Secondly, choosing stochastic process algebras as a widely accepted formalism, we study the compositionality of continuous PH distributions in order to support modelling...
Probability of stochastic processes and spacetime geometry
International Nuclear Information System (INIS)
Canessa, E.
2007-01-01
We made a first attempt to associate a probabilistic description of stochastic processes like birth-death processes with spacetime geometry in the Schwarzschild metrics on distance scales from the macro- to the micro-domains. We idealize an ergodic system in which system states communicate through a curved path composed of transition arrows where each arrow corresponds to a positive, analogous birth or death rate. (author)
International Nuclear Information System (INIS)
Gutierrez, R.; Gutierrez-Sanchez, R.; Nafidi, A.
2009-01-01
The main aim of this study is to model the trend of the evolution of the total stock of private petrol-driven cars. In Spain, as in other EU countries, this trend between 2000 and 2005 differed significantly from that observed from 1986 to 1999. Moreover, it varies greatly from that corresponding to the stock of diesel-driven cars, which consistently presents an exponential Gompertz-type increase. Spain constitutes a typical example of a failure to observe the maximum CO 2 emission levels assigned to it by 2012 under the Kyoto Protocol (1992); a significant percentage of these excess emissions is accounted for by the land transport sector, in general, and by the private cars subsector, in particular. This paper proposes a stochastic model based on a new non homogeneous stochastic gamma-type diffusion process which it is a stochastic version of a Gamma function type deterministic growth model considered in Skiadas . We describe its main probabilistic characteristics and establish a statistical methodology by which it can be fitted to real data and obtain medium-term forecasts that, in statistical terms, are quite accurate
A stochastic model for quantum measurement
International Nuclear Information System (INIS)
Budiyono, Agung
2013-01-01
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system. (paper)
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...
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...
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...
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...
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.
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.
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
be split into measurement noise and system noise. The system noise is used to compensate for those biological processes not explicitly described by the model. Many authors model conjugation by a simple mass action model first proposed by Levin et al. (1979). Also Michaelis-Menten dependence...... by an experiment conducted with E. faecium. In addition, we suggest that a 3rd order time-delay must be included in the model to account for the delay before a newly conjugated plasmid is expressed. A ML estimate of the parameters based on experimental data is found using the software CTSM. The conjugation rate......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 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...
Stochastic Models of Polymer Systems
2016-01-01
published in non-peer-reviewed journals (N/A for none) The dynamics of stochastic gradient algorithms (submitted); Noisy Hegselmann- Krause Systems...algorithms for big data applications. (2) We studied stochastic dynamics of polymer systems in the mean field limit. (3) We studied noisy Hegselmann- Krause
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.
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
Stochastic simplified modelling of abrasive waterjet footprints
Torrubia, P. Lozano; Axinte, D. A.
2016-01-01
Abrasive micro-waterjet processing is a non-conventional machining method that can be used to manufacture complex shapes in difficult-to-cut materials. Predicting the effect of the jet on the surface for a given set of machine parameters is a key element of controlling the process. However, the noise of the process is significant, making it difficult to design reliable jet-path strategies that produce good quality parts via controlled-depth milling. The process is highly unstable and has a strong random component that can affect the quality of the workpiece, especially in the case of controlled-depth milling. This study describes a method to predict the variability of the jet footprint for different jet feed speeds. A stochastic partial differential equation is used to describe the etched surface as the jet is moved over it, assuming that the erosion process can be divided into two main components: a deterministic part that corresponds to the average erosion of the jet and a stochastic part that accounts for the noise generated at different stages of the process. The model predicts the variability of the trench profiles to within less than 8%. These advances could enable abrasive micro-waterjet technology to be a suitable technology for controlled-depth milling. PMID:27118905
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 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.
Modelling the stochastic behaviour of primary nucleation.
Maggioni, Giovanni Maria; Mazzotti, Marco
2015-01-01
We study the stochastic nature of primary nucleation and how it manifests itself in a crystallisation process at different scales and under different operating conditions. Such characteristics of nucleation are evident in many experiments where detection times of crystals are not identical, despite identical experimental conditions, but instead are distributed around an average value. While abundant experimental evidence has been reported in the literature, a clear theoretical understanding and an appropriate modelling of this feature is still missing. In this contribution, we present two models describing a batch cooling crystallisation, where the interplay between stochastic nucleation and deterministic crystal growth is described differently in each. The nucleation and growth rates of the two models are estimated by a comprehensive set of measurements of paracetamol crystallisation from aqueous solution in a 1 mL vessel [Kadam et al., Chemical Engineering Science, 2012, 72, 10-19]. Both models are applied to the cooling crystallisation process above under different operating conditions, i.e. different volumes, initial concentrations, cooling rates. The advantages and disadvantages of the two approaches are illustrated and discussed, with particular reference to their use across scales of nucleation rate measured in very small crystallisers.
Medium Term Hydroelectric Production Planning - A Multistage Stochastic Optimization Model
Directory of Open Access Journals (Sweden)
BITA ANALUI
2014-06-01
Full Text Available Multistage stochastic programming is a key technology for making decisions over time in an uncertain environment. One of the promising areas in which this technology is implementable, is medium term planning of electricity production and trading where decision makers are typically faced with uncertain parameters (such as future demands and market prices that can be described by stochastic processes in discrete time. We apply this methodology to hydrosystem operation assuming random electricity prices and random inflows to the reservoir system. After describing the multistage stochastic model a simple case study is presented. In particular we use the model for pricing an electricity delivery contract in the framework of indifference pricing.
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...
Sun, Bo; Liao, Baopeng; Li, Mengmeng; Ren, Yi; Feng, Qiang; Yang, Dezhen
2018-03-27
In the degradation process, the randomness and multiplicity of variables are difficult to describe by mathematical models. However, they are common in engineering and cannot be neglected, so it is necessary to study this issue in depth. In this paper, the copper bending pipe in seawater piping systems is taken as the analysis object, and the time-variant reliability is calculated by solving the interference of limit strength and maximum stress. We did degradation experiments and tensile experiments on copper material, and obtained the limit strength at each time. In addition, degradation experiments on copper bending pipe were done and the thickness at each time has been obtained, then the response of maximum stress was calculated by simulation. Further, with the help of one kind of Monte Carlo method we propose, the time-variant reliability of copper bending pipe was calculated based on the stochastic degradation process and interference theory. Compared with traditional methods and verified by maintenance records, the results show that the time-variant reliability model based on the stochastic degradation process proposed in this paper has better applicability in the reliability analysis, and it can be more convenient and accurate to predict the replacement cycle of copper bending pipe under seawater-active corrosion.
Directory of Open Access Journals (Sweden)
Bo Sun
2018-03-01
Full Text Available In the degradation process, the randomness and multiplicity of variables are difficult to describe by mathematical models. However, they are common in engineering and cannot be neglected, so it is necessary to study this issue in depth. In this paper, the copper bending pipe in seawater piping systems is taken as the analysis object, and the time-variant reliability is calculated by solving the interference of limit strength and maximum stress. We did degradation experiments and tensile experiments on copper material, and obtained the limit strength at each time. In addition, degradation experiments on copper bending pipe were done and the thickness at each time has been obtained, then the response of maximum stress was calculated by simulation. Further, with the help of one kind of Monte Carlo method we propose, the time-variant reliability of copper bending pipe was calculated based on the stochastic degradation process and interference theory. Compared with traditional methods and verified by maintenance records, the results show that the time-variant reliability model based on the stochastic degradation process proposed in this paper has better applicability in the reliability analysis, and it can be more convenient and accurate to predict the replacement cycle of copper bending pipe under seawater-active corrosion.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Directory of Open Access Journals (Sweden)
A. Valor
2013-01-01
Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.
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…
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.
Numerical Simulation of the Heston Model under Stochastic Correlation
Directory of Open Access Journals (Sweden)
Long Teng
2017-12-01
Full Text Available Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.
Stochastic models for predicting pitting corrosion damage of HLRW containers
International Nuclear Information System (INIS)
Henshall, G.A.
1991-10-01
Stochastic models for predicting aqueous pitting corrosion damage of high-level radioactive-waste containers are described. These models could be used to predict the time required for the first pit to penetrate a container and the increase in the number of breaches at later times, both of which would be useful in the repository system performance analysis. Monte Carlo implementations of the stochastic models are described, and predictions of induction time, survival probability and pit depth distributions are presented. These results suggest that the pit nucleation probability decreases with exposure time and that pit growth may be a stochastic process. The advantages and disadvantages of the stochastic approach, methods for modeling the effects of environment, and plans for future work are discussed
A stochastic SIS epidemic model with vaccination
Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming
2017-11-01
In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.
Moment Closure for the Stochastic Logistic Model
National Research Council Canada - National Science Library
Singh, Abhyudai; Hespanha, Joao P
2006-01-01
..., which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model...
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
Stochastic modeling for environmental stress screening
Cha, Ji Hwan; Finkelstein, Maxim
2014-01-01
Environmental stress screening (ESS) of manufactured items is used to reduce the occurrence of future failures that are caused by latent defects by eliminating the items with these defects. Some practical descriptions of the relevant ESS procedures can be found in the literature; however, the appropriate stochastic modeling and the corresponding thorough analysis have not been reported. In this paper we develop a stochastic model for the ESS, analyze the effect of this operation o...
A stochastic model of enzyme kinetics
Stefanini, Marianne; Newman, Timothy; McKane, Alan
2003-10-01
Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.
Scalable inference for stochastic block models
Peng, Chengbin
2017-12-08
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference algorithms for such a model are increasingly limited due to their high time complexity and poor scalability. In this paper, we propose a multi-stage maximum likelihood approach to recover the latent parameters of the stochastic block model, in time linear with respect to the number of edges. We also propose a parallel algorithm based on message passing. Our algorithm can overlap communication and computation, providing speedup without compromising accuracy as the number of processors grows. For example, to process a real-world graph with about 1.3 million nodes and 10 million edges, our algorithm requires about 6 seconds on 64 cores of a contemporary commodity Linux cluster. Experiments demonstrate that the algorithm can produce high quality results on both benchmark and real-world graphs. An example of finding more meaningful communities is illustrated consequently in comparison with a popular modularity maximization algorithm.
Modelling Cow Behaviour Using Stochastic Automata
DEFF Research Database (Denmark)
Jónsson, Ragnar Ingi
This report covers an initial study on the modelling of cow behaviour using stochastic automata with the aim of detecting lameness. Lameness in cows is a serious problem that needs to be dealt with because it results in less profitable production units and in reduced quality of life...... for the affected livestock. By featuring training data consisting of measurements of cow activity, three different models are obtained, namely an autonomous stochastic automaton, a stochastic automaton with coinciding state and output and an autonomous stochastic automaton with coinciding state and output, all...... of which describe the cows' activity in the two regarded behavioural scenarios, non-lame and lame. Using the experimental measurement data the different behavioural relations for the two regarded behavioural scenarios are assessed. The three models comprise activity within last hour, activity within last...
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.
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...
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...
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...
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....... In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach....
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.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Valor, A.; Caleyo, F.; Alfonso, L.; Velázquez, J. C.; Hallen, J. M.
2013-01-01
The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure ...
The critical domain size of stochastic population models.
Reimer, Jody R; Bonsall, Michael B; Maini, Philip K
2017-02-01
Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.
Stochastic inverse problems: Models and metrics
International Nuclear Information System (INIS)
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-01-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds
Stochastic inverse problems: Models and metrics
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-03-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
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
Infinite-degree-corrected stochastic block model
DEFF Research Database (Denmark)
Herlau, Tue; Schmidt, Mikkel Nørgaard; Mørup, Morten
2014-01-01
In stochastic block models, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman [Karrer and Newman...... corrected stochastic block model as a nonparametric Bayesian model, incorporating a parameter to control the amount of degree correction that can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links...
Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations
Christensen, H. M.; Dawson, A.; Palmer, T.
2017-12-01
Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.
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 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
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
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.
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. PMID:27602000
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.
Random migration processes between two stochastic epidemic centers.
Sazonov, Igor; Kelbert, Mark; Gravenor, Michael B
2016-04-01
We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically. Copyright © 2016 Elsevier Inc. All rights reserved.
Stochastic volatility models and Kelvin waves
International Nuclear Information System (INIS)
Lipton, Alex; Sepp, Artur
2008-01-01
We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics
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.
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...
Compositional Modelling of Stochastic Hybrid Systems
Strubbe, S.N.
2005-01-01
In this thesis we present a modelling framework for compositional modelling of stochastic hybrid systems. Hybrid systems consist of a combination of continuous and discrete dynamics. The state space of a hybrid system is hybrid in the sense that it consists of a continuous component and a discrete
Weiss, Charles J.
2017-01-01
An introduction to digital stochastic simulations for modeling a variety of physical and chemical processes is presented. Despite the importance of stochastic simulations in chemistry, the prevalence of turn-key software solutions can impose a layer of abstraction between the user and the underlying approach obscuring the methodology being…
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.
Predicting Footbridge Response using Stochastic Load Models
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2013-01-01
Walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. are basically stochastic, although it is quite common to adapt deterministic models for these parameters. The present paper considers a stochastic approach to modeling the action of pedestrians, but when doing so...... decisions need to be made in terms of statistical distributions of walking parameters and in terms of the parameters describing the statistical distributions. The paper explores how sensitive computations of bridge response are to some of the decisions to be made in this respect. This is useful...
Stochastic resonance in biological nonlinear evolution models
Dunkel, Jörn; Hilbert, Stefan; Schimansky-Geier, Lutz; Hänggi, Peter
2004-05-01
We investigate stochastic resonance in the nonlinear, one-dimensional Fisher-Eigen model (FEM), which represents an archetypal model for biological evolution based on a global coupling scheme. In doing so we consider different periodically driven fitness functions which govern the evolution of a biological phenotype population. For the case of a simple harmonic fitness function we are able to derive the exact analytic solution for the asymptotic probability density. A distinct feature of this solution is a phase lag between the driving signal and the linear response of the system. Furthermore, for more complex systems a general perturbation theory (linear response approximation) is put forward. Using the latter approach, we investigate stochastic resonance in terms of the spectral amplification measure for a quadratic, a quartic single-peaked, and for a bistable fitness function. Our analytical results are also compared with those of detailed numerical simulations. Our findings vindicate that stochastic resonance does occur in these nonlinear, globally coupled biological systems.
The stochastic model of pitting corrosion of metals
You, Y. H.; Wang, B. R.; Hu, H. Y.
2017-12-01
Considering that pitting corrosion is a stochastic process, the purpose of this paper is to use stochastic theory to investigate the growth process of pitting corrosion of metals. Based on the mechanism of pit growth and nonequilibrium statistical theory, the time evolution equations of pit depth and corrosion rate are obtained, and the probability density function can be derived by solving Fock-Plank Equation. Subsequently, the failure probability or reliability of metals is calculated based on the weakest link model of pitting corrosion. Finally, the stochastic model is used on the aircraft aluminum alloy LD2. Furthermore, this methodology can be applied to analyze the reliability and predict the pitting life of metals.
Response spectrum analysis of a stochastic seismic model
International Nuclear Information System (INIS)
Kimura, Koji; Sakata, Masaru; Takemoto, Shinichiro.
1990-01-01
The stochastic response spectrum approach is presented for predicting the dynamic behavior of structures to earthquake excitation expressed by a random process, one of whose sample functions can be regarded as a recorded strong-motion earthquake accelerogram. The approach consists of modeling recorded ground motion by a random process and the root-mean-square response (rms) analysis of a single-degree-of-freedom system by using the moment equations method. The stochastic response spectrum is obtained as a plot of the maximum rms response versus the natural period of the system and is compared with the conventional response spectrum. (author)
Stochastic population and epidemic models persistence and extinction
Allen, Linda J S
2015-01-01
This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics ...
Stochastic modeling of virus capsid assembly pathways
Schwartz, Russell
2009-03-01
Virus capsids have become a key model system for understanding self-assembly due to their high complexity, robust and efficient assembly processes, and experimental tractability. Our ability to directly examine and manipulate capsid assembly kinetics in detail nonetheless remains limited, creating a need for computer models that can infer experimentally inaccessible features of the assembly process and explore the effects of hypothetical manipulations on assembly trajectories. We have developed novel algorithms for stochastic simulation of capsid assembly [1,2] that allow us to model capsid assembly over broad parameter spaces [3]. We apply these methods to study the nature of assembly pathway control in virus capsids as well as their sensitivity to assembly conditions and possible experimental interventions. [4pt] [1] F. Jamalyaria, R. Rohlfs, and R. Schwartz. J Comp Phys 204, 100 (2005). [0pt] [2] N. Misra and R. Schwartz. J Chem Phys 129, in press (2008). [0pt] [3] B. Sweeney, T. Zhang, and R. Schwartz. Biophys J 94, 772 (2008).
Reconstructing nonlinear dynamic models of gene regulation using stochastic sampling
Directory of Open Access Journals (Sweden)
Reinelt Gerhard
2009-12-01
Full Text Available Abstract Background The reconstruction of gene regulatory networks from time series gene expression data is one of the most difficult problems in systems biology. This is due to several reasons, among them the combinatorial explosion of possible network topologies, limited information content of the experimental data with high levels of noise, and the complexity of gene regulation at the transcriptional, translational and post-translational levels. At the same time, quantitative, dynamic models, ideally with probability distributions over model topologies and parameters, are highly desirable. Results We present a novel approach to infer such models from data, based on nonlinear differential equations, which we embed into a stochastic Bayesian framework. We thus address both the stochasticity of experimental data and the need for quantitative dynamic models. Furthermore, the Bayesian framework allows it to easily integrate prior knowledge into the inference process. Using stochastic sampling from the Bayes' posterior distribution, our approach can infer different likely network topologies and model parameters along with their respective probabilities from given data. We evaluate our approach on simulated data and the challenge #3 data from the DREAM 2 initiative. On the simulated data, we study effects of different levels of noise and dataset sizes. Results on real data show that the dynamics and main regulatory interactions are correctly reconstructed. Conclusions Our approach combines dynamic modeling using differential equations with a stochastic learning framework, thus bridging the gap between biophysical modeling and stochastic inference approaches. Results show that the method can reap the advantages of both worlds, and allows the reconstruction of biophysically accurate dynamic models from noisy data. In addition, the stochastic learning framework used permits the computation of probability distributions over models and model parameters
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
Population density equations for stochastic processes with memory kernels
Lai, Yi Ming; de Kamps, Marc
2017-06-01
We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.
Population density equations for stochastic processes with memory kernels.
Lai, Yi Ming; de Kamps, Marc
2017-06-01
We present a method for solving population density equations (PDEs)--a mean-field technique describing homogeneous populations of uncoupled neurons-where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation-a recent result from random network theory-describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.
Multiple-scale stochastic processes: Decimation, averaging and beyond
Energy Technology Data Exchange (ETDEWEB)
Bo, Stefano, E-mail: stefano.bo@nordita.org [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Celani, Antonio [Quantitative Life Sciences, The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 - Trieste (Italy)
2017-02-07
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.
On the Robustness of Temporal Properties for Stochastic Models
Directory of Open Access Journals (Sweden)
Ezio Bartocci
2013-08-01
Full Text Available Stochastic models such as Continuous-Time Markov Chains (CTMC and Stochastic Hybrid Automata (SHA are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling is the model checking problem. i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process. However, one may not only be interested in the notion of satisfiability, but also in the capacity of a system to mantain a particular emergent behaviour unaffected by the perturbations, caused e.g. from extrinsic noise, or by possible small changes in the model parameters. To address this issue, researchers from the verification community have recently proposed several notions of robustness for temporal logic providing suitable definitions of distance between a trajectory of a (deterministic dynamical system and the boundaries of the set of trajectories satisfying the property of interest. The contributions of this paper are twofold. First, we extend the notion of robustness to stochastic systems, showing that this naturally leads to a distribution of robustness scores. By discussing two examples, we show how to approximate the distribution of the robustness score and its key indicators: the average robustness and the conditional average robustness. Secondly, we show how to combine these indicators with the satisfaction probability to address the system design problem, where the goal is to optimize some control parameters of a stochastic model in order to best maximize robustness of the desired specifications.
Stochastic resonance in models of neuronal ensembles
International Nuclear Information System (INIS)
Chialvo, D.R.; Longtin, A.; Mueller-Gerkin, J.
1997-01-01
Two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time-varying inputs are considered. It is shown, using theoretical arguments and numerical simulations, that the nonmonotonic behavior with increasing noise of the correlation measures used for the so-called aperiodic stochastic resonance (ASR) scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems. Rather, ASR with slowly varying signals is more properly interpreted as linearization by noise. Consequently, the broadening of the open-quotes resonance curveclose quotes in the multineuron stochastic resonance without tuning scenario can also be explained by this linearization. Computation of the input-output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise-induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise. Thus, our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals. It also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime. Finally, we show that the inclusion of a refractory period in the spike-detection scheme produces a better correlation between instantaneous firing rate and input signal. copyright 1997 The American Physical Society
Reflected stochastic differential equation models for constrained animal movement
Hanks, Ephraim M.; Johnson, Devin S.; Hooten, Mevin B.
2017-01-01
Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.
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...
Normal Forms for Reduced Stochastic Climate Models
Franzke, C.; Majda, A.; Crommelin, D.
2009-04-01
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. The use of a few Empirical Orthogonal Functions (EOF) depending on observational data to span the low-frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low- and high-frequency subspaces of the dynamics. It will be shown that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. For a single low-frequency variable the dyad interactions and climatological linear operator alone produce a normal form with CAM noise from advection of the large-scales by the small scales and simultaneously strong cubic damping. This normal form should prove useful for developing systematic regression fitting strategies for stochastic models of climate data. The validity of the one and two dimensional normal forms will be presented. Also the analytical PDF form for one-dimensional reduced models will be derived. This PDF can exhibit power-law decay only over a limited range and its ultimate decay is determined by the cubic damping. This cubic damping produces a Gaussian tail.
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.
Modeling animal movements using stochastic differential equations
Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie
2004-01-01
We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...
Vulnerability in a Stochastic Dynamic Model
Elbers, Chris; Gunning, Jan Willem
2003-01-01
Most measures of vulnerability are a-theoretic and essentially static. In this paper we use a stochastic Ramsey model to find a household's optimal welfare and we measure vulnerability as the shortfall from the welfare attained if the household consumed permanently at the poverty line. The results
Stochastic Modeling Of Wind Turbine Drivetrain Components
DEFF Research Database (Denmark)
Rafsanjani, Hesam Mirzaei; Sørensen, John Dalsgaard
2014-01-01
reliable components are needed for wind turbine. In this paper focus is on reliability of critical components in drivetrain such as bearings and shafts. High failure rates of these components imply a need for more reliable components. To estimate the reliability of these components, stochastic models...
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.
Stochastic modelling of migration from polyolefins
Helmroth, I.E.; Varekamp, C.; Dekker, M.
2005-01-01
A method is presented to predict diffusion coefficients in polyolefins using stochastic modelling. A large number of experimental diffusion coefficients, published in the literature as one dataset, was used to derive probability distributions of diffusion coefficients in the polymers low-density
Stochastic modeling of sunshine number data
Energy Technology Data Exchange (ETDEWEB)
Brabec, Marek, E-mail: mbrabec@cs.cas.cz [Department of Nonlinear Modeling, Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou vezi 2, 182 07 Prague 8 (Czech Republic); Paulescu, Marius [Physics Department, West University of Timisoara, V. Parvan 4, 300223 Timisoara (Romania); Badescu, Viorel [Candida Oancea Institute, Polytechnic University of Bucharest, Spl. Independentei 313, 060042 Bucharest (Romania)
2013-11-13
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Stochastic modeling of sunshine number data
International Nuclear Information System (INIS)
Brabec, Marek; Paulescu, Marius; Badescu, Viorel
2013-01-01
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Stochastic Energetics for Non-Gaussian Processes
Kanazawa, Kiyoshi; Sagawa, Takahiro; Hayakawa, Hisao
2012-05-01
By introducing a new stochastic integral, we investigate the energetics of classical stochastic systems driven by non-Gaussian white noises. In particular, we introduce a decomposition of the total energy difference into the work and the heat for each trajectory, and derive a formula to calculate the heat from experimental data on the dynamics. We apply our formulation and results to a Langevin system driven by a Poisson noise.
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
Stochastic forward and inverse groundwater flow and solute transport modeling
Janssen, G.M.C.M.
2008-01-01
Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers
This thesis offers three new approaches that contribute
2013-09-30
picture of ENSO-driven autoregressive models for North Pacific SST variability, providing evidence that intermittent processes, such as variability of...intermittent aspects (i) and (ii) are achieved by developing a simple stochastic parameterization for the unresolved details of synoptic -scale...stochastic parameterization of synoptic scale activity to build a stochastic skeleton model for the MJO; this is the first low order model of the MJO which
Filtering and identification of stochastic volatility for parabolic type factor models
Aihara, ShinIchi; Bagchi, Arunabha
2006-01-01
We consider the dynamics of forward rate process which is modeled by a parabolic type infinite-dimensional factor model with stochastic volatility. The parameters included in the stochastic volatility dynamics are estimated from the factor process as the observation data. Based on the maximum
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
Model predictive control classical, robust and stochastic
Kouvaritakis, Basil
2016-01-01
For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplic...
Stochastic text models for music categorization
Pérez Sancho, Carlos; Rizo Valero, David; Iñesta Quereda, José Manuel
2008-01-01
Music genre meta-data is of paramount importance for the organization of music repositories. People use genre in a natural way when entering a music store or looking into music collections. Automatic genre classification has become a popular topic in music information retrieval research. This work brings to symbolic music recognition some technologies, like the stochastic language models, already successfully applied to text categorization. In this work we model chord progressions and melodie...
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.
A hierarchical stochastic model for bistable perception.
Directory of Open Access Journals (Sweden)
Stefan Albert
2017-11-01
Full Text Available Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM, which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group
A hierarchical stochastic model for bistable perception.
Albert, Stefan; Schmack, Katharina; Sterzer, Philipp; Schneider, Gaby
2017-11-01
Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM) for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM), which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group differences to
Time-variant reliability assessment through equivalent stochastic process transformation
International Nuclear Information System (INIS)
Wang, Zequn; Chen, Wei
2016-01-01
Time-variant reliability measures the probability that an engineering system successfully performs intended functions over a certain period of time under various sources of uncertainty. In practice, it is computationally prohibitive to propagate uncertainty in time-variant reliability assessment based on expensive or complex numerical models. This paper presents an equivalent stochastic process transformation approach for cost-effective prediction of reliability deterioration over the life cycle of an engineering system. To reduce the high dimensionality, a time-independent reliability model is developed by translating random processes and time parameters into random parameters in order to equivalently cover all potential failures that may occur during the time interval of interest. With the time-independent reliability model, an instantaneous failure surface is attained by using a Kriging-based surrogate model to identify all potential failure events. To enhance the efficacy of failure surface identification, a maximum confidence enhancement method is utilized to update the Kriging model sequentially. Then, the time-variant reliability is approximated using Monte Carlo simulations of the Kriging model where system failures over a time interval are predicted by the instantaneous failure surface. The results of two case studies demonstrate that the proposed approach is able to accurately predict the time evolution of system reliability while requiring much less computational efforts compared with the existing analytical approach. - Highlights: • Developed a new approach for time-variant reliability analysis. • Proposed a novel stochastic process transformation procedure to reduce the dimensionality. • Employed Kriging models with confidence-based adaptive sampling scheme to enhance computational efficiency. • The approach is effective for handling random process in time-variant reliability analysis. • Two case studies are used to demonstrate the efficacy
Model tracking dual stochastic controller design under irregular internal noises
International Nuclear Information System (INIS)
Lee, Jong Bok; Heo, Hoon; Cho, Yun Hyun; Ji, Tae Young
2006-01-01
Although many methods about the control of irregular external noise have been introduced and implemented, it is still necessary to design a controller that will be more effective and efficient methods to exclude for various noises. Accumulation of errors due to model tracking, internal noises (thermal noise, shot noise and l/f noise) that come from elements such as resistor, diode and transistor etc. in the circuit system and numerical errors due to digital process often destabilize the system and reduce the system performance. New stochastic controller is adopted to remove those noises using conventional controller simultaneously. Design method of a model tracking dual controller is proposed to improve the stability of system while removing external and internal noises. In the study, design process of the model tracking dual stochastic controller is introduced that improves system performance and guarantees robustness under irregular internal noises which can be created internally. The model tracking dual stochastic controller utilizing F-P-K stochastic control technique developed earlier is implemented to reveal its performance via simulation
Stochastic renewal process models for estimation of damage cost over the life-cycle of a structure
Pandey, Mahesh D.; van der Weide, J.A.M.
2017-01-01
In the life-cycle cost analysis of a structure, the total cost of damage caused by external hazards like earthquakes, wind storms and flood is an important but highly uncertain component. In the literature, the expected damage cost is typically analyzed under the assumption of either the homogeneous Poisson process or the renewal process in an infinite time horizon (i.e., asymptotic solution). The paper reformulates the damage cost estimation problem as a compound renewal process and derives ...
Stochastic Spectral Descent for Discrete Graphical Models
International Nuclear Information System (INIS)
Carlson, David; Hsieh, Ya-Ping; Collins, Edo; Carin, Lawrence; Cevher, Volkan
2015-01-01
Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.
Brain-inspired Stochastic Models and Implementations
Al-Shedivat, Maruan
2015-05-12
One of the approaches to building artificial intelligence (AI) is to decipher the princi- ples of the brain function and to employ similar mechanisms for solving cognitive tasks, such as visual perception or natural language understanding, using machines. The recent breakthrough, named deep learning, demonstrated that large multi-layer networks of arti- ficial neural-like computing units attain remarkable performance on some of these tasks. Nevertheless, such artificial networks remain to be very loosely inspired by the brain, which rich structures and mechanisms may further suggest new algorithms or even new paradigms of computation. In this thesis, we explore brain-inspired probabilistic mechanisms, such as neural and synaptic stochasticity, in the context of generative models. The two questions we ask here are: (i) what kind of models can describe a neural learning system built of stochastic components? and (ii) how can we implement such systems e ̆ciently? To give specific answers, we consider two well known models and the corresponding neural architectures: the Naive Bayes model implemented with a winner-take-all spiking neural network and the Boltzmann machine implemented in a spiking or non-spiking fashion. We propose and analyze an e ̆cient neuromorphic implementation of the stochastic neu- ral firing mechanism and study the e ̄ects of synaptic unreliability on learning generative energy-based models implemented with neural networks.
Stochastic Modelling of Energy Systems
DEFF Research Database (Denmark)
Andersen, Klaus Kaae
2001-01-01
In this thesis dynamic models of typical components in Danish heating systems are considered. Emphasis is made on describing and evaluating mathematical methods for identification of such models, and on presentation of component models for practical applications. The thesis consists of seven...... of component models, such as e.g. heat exchanger and valve models, adequate for system simulations. Furthermore, the thesis demonstrates and discusses the advantages and disadvantages of using statistical methods in conjunction with physical knowledge in establishing adequate component models of heating...... research papers (case studies) together with a summary report. Each case study takes it's starting point in typical heating system components and both, the applied mathematical modelling methods and the application aspects, are considered. The summary report gives an introduction to the scope...
Verification and Planning for Stochastic Processes with Asynchronous Events
National Research Council Canada - National Science Library
Younes, Hakan L
2005-01-01
.... The most common assumption is that of history-independence: the Markov assumption. In this thesis, the author considers the problems of verification and planning for stochastic processes with asynchronous events, without relying on the Markov assumption...
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.
Stochastic Climate Forcing for Ice-Sheet Models
Nuterman, Roman; Jochum, Markus
2017-04-01
Climate oscillations from glacial periods, with large parts of the continents covered with ice, to warm interglacials like the present one, are observed in various paleoclimatic records over the past few million years. According to Milankovitch theory, which is commonly assumed, these glacial cycles are linked to changes in insolation due to periodic changes of external earth-orbital forcing. However, this relationship is far from understood, because the insolation variations are so small that enhancing feedbacks must be at play. Moreover, there are several shortcomings in the Milankovitch theory: first, the duration of the glacial cycles changed at the so-called Mid-Pleistocene transition from 41,000 years to approximately 100,000 years and second, the interglacial of 400,000 years ago should not have happened. Thus, the current phasing and magnitude of the glacial cycles are far from being well understood and the external perturbation might only play a minor role in comparison to internal stochastic variations or internal oscillations. Although modern Ice-Sheet Models (ISM) are able to simulate evolution of ice-sheets at the entire glacial or interglacial time scales, the state-of-the-art Earth System Models (ESM) are too computationally expensive for such long integrations. Therefore, a constant climate forcing is usually used in the ice-sheet models. However, this approach does not take into account the stochastic nature of climate. At the same time, ESM models provide valuable information on natural climate variability, which then can be used for building stochastic climate models able to generate both continuous and discrete climate variables with stochastic atmospheric processes. In this study, we present a stochastic climate model, built from large sets of Community Earth System Model (CESM) integrations with both internal and external climate forcing, and able to generate synthetic climate forcing (such as temperature and precipitation fields) of any
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...
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...
GEMFsim: A Stochastic Simulator for the Generalized Epidemic Modeling Framework
Sahneh, Faryad Darabi; Vajdi, Aram; 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 ...
Stochastic Modelling of Seafloor Morphology
1990-06-01
year of a grad students life into one of the most enjoyable. I also thank Mom, Dad, Barbi , Ellie, Robbie, Dick and Jean, Trudy and Will, Grandma and...1981; 1986] and Sinton et al. [ 19831 on the basis of variations in crystal fractionation throughout the evolution of the Galapagos 95.50 W...propagator. It is also consistent with the tectonic model proposed by Kleinrock and Hey [1989] for the evolution of the same propagator. In their model
Stochastic models for time series
Doukhan, Paul
2018-01-01
This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit ...
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
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......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...
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
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
Zacharuk, Matthias; Dolaptchiev, Stamen; Achatz, Ulrich; Timofeyev, Ilya
2017-04-01
Due to the finite spatial resolution in numerical atmospheric models, subgrid-scale (SGS) processes arise. A SGS parameterization of these excluded processes might improve the model on all scales. In this study we present a model derived parameterization of these processes for the one dimensional shallow water equations. 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 stochastic MTV SGS parameterization can be derived from the model equation, which is the advantage of this method compared to others. So far the 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). To apply the method onto the one the dimensional shallow water equations, we choose a local approach of the fine variable self-interactions. With this, we are able to derive a local SGS parameterization using MTV's method leading to a closed model wrt. the coarse variable. We show, that this model is able to fix the energy decrease for high wave numbers which appears at the coarse resolution model with neglected SGS parameterization. In the future we plan to extend the model to two dimensions and multiple layers. Perspectively, the method can be used to derive a
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. 2009 Elsevier Ltd. All rights reserved.
Stochastic Model of TCP SYN Attacks
Simona Ramanauskaitė; Antanas Čenys
2011-01-01
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...
Simulating biological processes: stochastic physics from whole cells to colonies
Earnest, Tyler M.; Cole, John A.; Luthey-Schulten, Zaida
2018-05-01
The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a ‘minimal cell’. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.
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.
Energy Technology Data Exchange (ETDEWEB)
Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 Havana (Cuba); Caleyo, F. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)]. E-mail: fcaleyo@gmail.com; Alfonso, L. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Rivas, D. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Hallen, J.M. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)
2007-02-15
In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion.
Stem Cell Differentiation as a Non-Markov Stochastic Process.
Stumpf, Patrick S; Smith, Rosanna C G; Lenz, Michael; Schuppert, Andreas; Müller, Franz-Josef; Babtie, Ann; Chan, Thalia E; Stumpf, Michael P H; Please, Colin P; Howison, Sam D; Arai, Fumio; MacArthur, Ben D
2017-09-27
Pluripotent stem cells can self-renew in culture and differentiate along all somatic lineages in vivo. While much is known about the molecular basis of pluripotency, the mechanisms of differentiation remain unclear. Here, we profile individual mouse embryonic stem cells as they progress along the neuronal lineage. We observe that cells pass from the pluripotent state to the neuronal state via an intermediate epiblast-like state. However, analysis of the rate at which cells enter and exit these observed cell states using a hidden Markov model indicates the presence of a chain of unobserved molecular states that each cell transits through stochastically in sequence. This chain of hidden states allows individual cells to record their position on the differentiation trajectory, thereby encoding a simple form of cellular memory. We suggest a statistical mechanics interpretation of these results that distinguishes between functionally distinct cellular "macrostates" and functionally similar molecular "microstates" and propose a model of stem cell differentiation as a non-Markov stochastic process. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power
DEFF Research Database (Denmark)
Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte
2010-01-01
This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...
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...
Modeling stochastic frontier based on vine copulas
Constantino, Michel; Candido, Osvaldo; Tabak, Benjamin M.; da Costa, Reginaldo Brito
2017-11-01
This article models a production function and analyzes the technical efficiency of listed companies in the United States, Germany and England between 2005 and 2012 based on the vine copula approach. Traditional estimates of the stochastic frontier assume that data is multivariate normally distributed and there is no source of asymmetry. The proposed method based on vine copulas allow us to explore different types of asymmetry and multivariate distribution. Using data on product, capital and labor, we measure the relative efficiency of the vine production function and estimate the coefficient used in the stochastic frontier literature for comparison purposes. This production vine copula predicts the value added by firms with given capital and labor in a probabilistic way. It thereby stands in sharp contrast to the production function, where the output of firms is completely deterministic. The results show that, on average, S&P500 companies are more efficient than companies listed in England and Germany, which presented similar average efficiency coefficients. For comparative purposes, the traditional stochastic frontier was estimated and the results showed discrepancies between the coefficients obtained by the application of the two methods, traditional and frontier-vine, opening new paths of non-linear research.
Modeling and Prediction Using Stochastic Differential Equations
DEFF Research Database (Denmark)
Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp
2016-01-01
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......) for modeling and forecasting. It is argued that this gives models and predictions which better reflect reality. The SDE approach also offers a more adequate framework for modeling and a number of efficient tools for model building. A software package (CTSM-R) for SDE-based modeling is briefly described....... 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...
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......, pedestrian mass, dynamic load factor, etc. to be random variables. By this approach a probability distribution function of bridge response is calculated. The paper explores how sensitive estimates of probability distribution functions of bridge response are to some of the decisions to be made when modelling...
Can Household Benefit from Stochastic Programming Models?
DEFF Research Database (Denmark)
Rasmussen, Kourosh Marjani; Madsen, Claus A.; Poulsen, Rolf
2014-01-01
The Danish mortgage market is large and sophisticated. However, most Danish mortgage banks advise private home-owners based on simple, if sensible, rules of thumb. In recent years a number of papers (from Nielsen and Poulsen in J Econ Dyn Control 28:1267–1289, 2004 over Rasmussen and Zenios in J...... Risk 10:1–18, 2007 to Pedersen et al. in Ann Oper Res, 2013) have suggested a model-based, stochastic programming approach to mortgage choice. This paper gives an empirical comparison of performance over the period 2000–2010 of the rules of thumb to the model-based strategies. While the rules of thumb...
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.
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
Lévy Véhel, J.
2013-09-01
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.
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
Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation
Kalliadasis, Serafim; Gomes, Susana; Papageorgiou, Demetrios; Pavliotis, Greg; Pradas, Marc
2017-11-01
We present a novel methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strategy is then based on two steps: first, stabilize the zero solution of the deterministic part and, second, control the roughness of the stochastic linear equation. We consider both periodic controls and point actuated ones, observing in all cases that the second moment of the solution evolves in time according to a power-law until it saturates at the desired controlled value. Furthermore, our control framework allows us to force the interfaces to have a prescribed shape. We observe from our numerical experiments that our results are valid for different types of nonlinearity (in particular, the Burgers and KPZ ones) as well as white and coloured noise.
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.
Diffusive processes in a stochastic magnetic field
International Nuclear Information System (INIS)
Wang, H.; Vlad, M.; Vanden Eijnden, E.; Spineanu, F.; Misguich, J.H.; Balescu, R.
1995-01-01
The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle's trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works
Stochastic modeling of central apnea events in preterm infants
Clark, Matthew T.; Delos, John B.; Lake, Douglas E.; Lee, Hoshik; Fairchild, Karen D.; Kattwinkel, John; Moorman, J. Randall
2016-01-01
Summary A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the NICU. It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 hours) to very unstable (with an average lifetime of 10 seconds). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm – stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events – may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge. PMID:26963049
Stochastic modeling of central apnea events in preterm infants
International Nuclear Information System (INIS)
Clark, Matthew T; Lake, Douglas E; Randall Moorman, J; Delos, John B; Lee, Hoshik; Fairchild, Karen D; Kattwinkel, John
2016-01-01
A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm—stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events—may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge. (paper)
Stochastic modeling of central apnea events in preterm infants.
Clark, Matthew T; Delos, John B; Lake, Douglas E; Lee, Hoshik; Fairchild, Karen D; Kattwinkel, John; Moorman, J Randall
2016-04-01
A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm-stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events-may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge.
Stochastic model of Rayleigh-Taylor turbulent mixing
International Nuclear Information System (INIS)
Abarzhi, S.I.; Cadjan, M.; Fedotov, S.
2007-01-01
We propose a stochastic model to describe the random character of the dissipation process in Rayleigh-Taylor turbulent mixing. The parameter alpha, used conventionally to characterize the mixing growth-rate, is not a universal constant and is very sensitive to the statistical properties of the dissipation. The ratio between the rates of momentum loss and momentum gain is the statistic invariant and a robust parameter to diagnose with or without turbulent diffusion accounted for
Sensitivity Study of Stochastic Walking Load Models
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2010-01-01
is to employ a stochastic load model accounting for mean values and standard deviations for the walking load parameters, and to use this as a basis for estimation of structural response. This, however, requires decisions to be made in terms of statistical istributions and their parameters, and the paper...... 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...
DEFF Research Database (Denmark)
Sommer, Stefan Horst; Svane, Anne Marie
2017-01-01
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in...
A stochastic model of AIDS and condom use
Dalal, Nirav; Greenhalgh, David; Mao, Xuerong
2007-01-01
In this paper we introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation which is standard in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system.
Lognormal-like statistics of a stochastic squeeze process
Shapira, Dekel; Cohen, Doron
2017-10-01
We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate w and the angular diffusion coefficient D . We carry out an exact analysis to determine the drift and the diffusion coefficient of log(r ) , where r is the radial coordinate. The results go beyond the heuristic lognormal description that is implied by the central limit theorem. Contrary to the common "quantum Zeno" approximation, the radial diffusion is not simply Dr=(1 /8 ) w2/D but has a nonmonotonic dependence on w /D . Furthermore, the calculation of the radial moments is dominated by the far non-Gaussian tails of the log(r ) distribution.
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
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
Using Stochastic Model Checking to Provision Complex Business Services
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2012-01-01
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...... 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......-deterministic branching and reward annotations. We then develop an algorithm for the efficient translation of these models into the guarded command language used by the model checker PRISM, in turn enabling model checking of BPMN processes and allowing for the calculation of a wide range of quantitative properties...
Data-driven stochastic modelling of zebrafish locomotion.
Zienkiewicz, Adam; Barton, David A W; Porfiri, Maurizio; di Bernardo, Mario
2015-11-01
In this work, we develop a data-driven modelling framework to reproduce the locomotion of fish in a confined environment. Specifically, we highlight the primary characteristics of the motion of individual zebrafish (Danio rerio), and study how these can be suitably encapsulated within a mathematical framework utilising a limited number of calibrated model parameters. Using data captured from individual zebrafish via automated visual tracking, we develop a model using stochastic differential equations and describe fish as a self propelled particle moving in a plane. Based on recent experimental evidence of the importance of speed regulation in social behaviour, we extend stochastic models of fish locomotion by introducing experimentally-derived processes describing dynamic speed regulation. Salient metrics are defined which are then used to calibrate key parameters of coupled stochastic differential equations, describing both speed and angular speed of swimming fish. The effects of external constraints are also included, based on experimentally observed responses. Understanding the spontaneous dynamics of zebrafish using a bottom-up, purely data-driven approach is expected to yield a modelling framework for quantitative investigation of individual behaviour in the presence of various external constraints or biological assays.
Stochastic modeling of financial electricity contracts
International Nuclear Information System (INIS)
Benth, Fred Espen; Koekebakker, Steen
2008-01-01
We discuss the modeling of electricity contracts traded in many deregulated power markets. These forward/futures type contracts deliver (either physically or financially) electricity over a specified time period, and is frequently referred to as swaps since they in effect represent an exchange of fixed for floating electricity price. We propose to use the Heath-Jarrow-Morton approach to model swap prices since the notion of a spot price is not easily defined in these markets. For general stochastic dynamical models, we connect the spot price, the instantaneous-delivery forward price and the swap price, and analyze two different ways to apply the Heath-Jarrow-Morton approach to swap pricing: Either one specifies a dynamics for the non-existing instantaneous-delivery forwards and derives the implied swap dynamics, or one models directly on the swaps. The former is shown to lead to quite complicated stochastic models for the swap price, even when the forward dynamics is simple. The latter has some theoretical problems due to a no-arbitrage condition that has to be satisfied for swaps with overlapping delivery periods. To overcome this problem, a practical modeling approach is analyzed. The market is supposed only to consist of non-overlapping swaps, and these are modelled directly. A thorough empirical study is performed using data collected from Nord Pool. Our investigations demonstrate that it is possible to state reasonable models for the swap price dynamics which is analytically tractable for risk management and option pricing purposes, however, this is an area of further research. (author)
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...
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 ...
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 modelling in design of mechanical properties of nanometals
International Nuclear Information System (INIS)
Tengen, T.B.; Wejrzanowski, T.; Iwankiewicz, R.; Kurzydlowski, K.J.
2010-01-01
Polycrystalline nanometals are being fabricated through different processing routes and conditions. The consequence is that nanometals having the same mean grain size may have different grain size dispersion and, hence, may have different material properties. This has often led to conflicting reports from both theoretical and experimental findings about the evolutions of the mechanical properties of nanomaterials. The present paper employs stochastic model to study the impact of microstructure evolution during grain growth on the mechanical properties of polycrystalline nanometals. The stochastic model for grain growth and the stochastic model for changes in mechanical properties of nanomaterials are proposed. The model for the mechanical properties developed is tested on aluminium samples.Many salient features of the mechanical properties of the aluminium samples are revealed. The results show that the different mechanisms of grain growth impart different nature of response to the material mechanical properties. The conventional, homologous and anomalous temperature dependences of the yield stress have also been revealed to be due to different nature of interactions of the microstructures during evolution.
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 t^{1/2}. 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.
A delay financial model with stochastic volatility; martingale method
Lee, Min-Ku; Kim, Jeong-Hoon; Kim, Joocheol
2011-08-01
In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under this hybrid model. The core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term. Subsequently, a correction effect on the European option price is demonstrated both theoretically and numerically for a good agreement with practical results.
A Constructive Sharp Approach to Functional Quantization of Stochastic Processes
Junglen, Stefan; Luschgy, Harald
2010-01-01
We present a constructive approach to the functional quantization problem of stochastic processes, with an emphasis on Gaussian processes. The approach is constructive, since we reduce the infinite-dimensional functional quantization problem to a finite-dimensional quantization problem that can be solved numerically. Our approach achieves the sharp rate of the minimal quantization error and can be used to quantize the path space for Gaussian processes and also, for example, Lévy processes.
SMART (Stochastic Model Acquisition with ReinforcemenT) learning agents: A preliminary report
Child, C. H. T.; Stathis, K.
2005-01-01
We present a framework for building agents that learn using SMART, a system that combines stochastic model acquisition with reinforcement learning to enable an agent to model its environment through experience and subsequently form action selection policies using the acquired model. We extend an existing algorithm for automatic creation of stochastic strips operators [9] as a preliminary method of environment modelling. We then define the process of generation of future states using these ope...
Optimal information diffusion in stochastic block models.
Curato, Gianbiagio; Lillo, Fabrizio
2016-09-01
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 for which 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.
Stochastic Modeling and Analysis of Power System with Renewable Generation
DEFF Research Database (Denmark)
Chen, Peiyuan
. With the increasing number of wind turbines (WTs) connected to distribution systems, network operators are concerned about how such a stochastic generation affects power losses of the network. Furthermore, the operators need to estimate how much and when the stochastic generation can reduce the loading of substation...... be achieved through a probabilistic analysis that takes into account the stochastic behavior of wind power generation (WPG) and load demand. Such a probabilistic analysis may help network operators to cut down the cost associated with system planning. Thus, the objective of this thesis is to develop...... stochastic models of renewable generation and load demand for the optimal operation and planning of modern distribution systems through a probabilistic approach. On the basis of statistical data, stochastic models of WPG, load and combined heat and power (CHP) generation are developed. The stochastic wind...
A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis
Directory of Open Access Journals (Sweden)
Linda J.S. Allen
2017-05-01
Full Text Available Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented. Specifically, models are formulated for continuous-time Markov chains and stochastic differential equations. Some well-known examples are used for illustration such as an SIR epidemic model and a host-vector malaria model. Analytical methods for approximating the probability of a disease outbreak are also discussed. Keywords: Branching process, Continuous-time Markov chain, Minor outbreak, Stochastic differential equation, 2000 MSC: 60H10, 60J28, 92D30
Learning Theory Estimates with Observations from General Stationary Stochastic Processes.
Hang, Hanyuan; Feng, Yunlong; Steinwart, Ingo; Suykens, Johan A K
2016-12-01
This letter investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by general, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established. The obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization (ERM), least squares support vector machines (LS-SVMs) using given generic kernels, and SVMs using gaussian kernels for both least squares and quantile regression. It turns out that for independent and identically distributed (i.i.d.) processes, our learning rates for ERM recover the optimal rates. For non-i.i.d. processes, including geometrically [Formula: see text]-mixing Markov processes, geometrically [Formula: see text]-mixing processes with restricted decay, [Formula: see text]-mixing processes, and (time-reversed) geometrically [Formula: see text]-mixing processes, our learning rates for SVMs with gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates. For the remaining cases, our rates are at least close to the optimal rates. As a by-product, the assumed generalized Bernstein-type inequality also provides an interpretation of the so-called effective number of observations for various mixing processes.
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...
An adaptive stochastic model for financial markets
International Nuclear Information System (INIS)
Hernández, Juan Antonio; Benito, Rosa Marı´a; Losada, Juan Carlos
2012-01-01
An adaptive stochastic model is introduced to simulate the behavior of real asset markets. The model adapts itself by changing its parameters automatically on the basis of the recent historical data. The basic idea underlying the model is that a random variable uniformly distributed within an interval with variable extremes can replicate the histograms of asset returns. These extremes are calculated according to the arrival of new market information. This adaptive model is applied to the daily returns of three well-known indices: Ibex35, Dow Jones and Nikkei, for three complete years. The model reproduces the histograms of the studied indices as well as their autocorrelation structures. It produces the same fat tails and the same power laws, with exactly the same exponents, as in the real indices. In addition, the model shows a great adaptation capability, anticipating the volatility evolution and showing the same volatility clusters observed in the assets. This approach provides a novel way to model asset markets with internal dynamics which changes quickly with time, making it impossible to define a fixed model to fit the empirical observations.
Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson
Directory of Open Access Journals (Sweden)
Bullinger Eric
2006-12-01
Full Text Available Abstract "Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background.
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....
Approximate models for broken clouds in stochastic radiative transfer theory
International Nuclear Information System (INIS)
Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas
2014-01-01
This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models
Disentangling the importance of ecological niches from stochastic processes across scales
Chase, Jonathan M.; Myers, Jonathan A.
2011-01-01
Deterministic theories in community ecology suggest that local, niche-based processes, such as environmental filtering, biotic interactions and interspecific trade-offs largely determine patterns of species diversity and composition. In contrast, more stochastic theories emphasize the importance of chance colonization, random extinction and ecological drift. The schisms between deterministic and stochastic perspectives, which date back to the earliest days of ecology, continue to fuel contemporary debates (e.g. niches versus neutrality). As illustrated by the pioneering studies of Robert H. MacArthur and co-workers, resolution to these debates requires consideration of how the importance of local processes changes across scales. Here, we develop a framework for disentangling the relative importance of deterministic and stochastic processes in generating site-to-site variation in species composition (β-diversity) along ecological gradients (disturbance, productivity and biotic interactions) and among biogeographic regions that differ in the size of the regional species pool. We illustrate how to discern the importance of deterministic processes using null-model approaches that explicitly account for local and regional factors that inherently create stochastic turnover. By embracing processes across scales, we can build a more synthetic framework for understanding how niches structure patterns of biodiversity in the face of stochastic processes that emerge from local and biogeographic factors. PMID:21768151
Interplanetary Alfvenic fluctuations: A stochastic model
International Nuclear Information System (INIS)
Barnes, A.
1981-01-01
The strong alignment of the average directions of minimum magnetic variance and mean magnetic field in interplanetary Alfvenic fluctuations is inconsistent with the usual wave-propagation models. We investigate the concept of minimum variance for nonplanar Alfvenic fluctuations in which the field direction varies stochastically. It is found that the tendency of the minimum variance and mean field directions to be aligned may be purely a consequence of the randomness of the field direction. In particular, a well-defined direction of minimum variance does not imply that the fluctuations are necessarily planar. The fluctuation power spectrum is a power law for frequencies much higher than the inverse of the correlation time. The probability distribution of directions a randomly fluctuating field of constant magnitude is calculated. A new approach for observational studies of interplanetary fluctuations is suggested
A stochastic surplus production model in continuous time
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte
2017-01-01
surplus production model in continuous time (SPiCT), which in addition to stock dynamics also models the dynamics of the fisheries. This enables error in the catch process to be reflected in the uncertainty of estimated model parameters and management quantities. Benefits of the continuous-time state......Surplus production modelling has a long history as a method for managing data-limited fish stocks. Recent advancements have cast surplus production models as state-space models that separate random variability of stock dynamics from error in observed indices of biomass. We present a stochastic...... and improve estimation of reference points relative to discrete-time analysis of aggregated annual data. Finally, subannual data from five North Sea stocks are analysed with particular focus on using residual analysis to diagnose model insufficiencies and identify necessary model extensions such as robust...
A spatially structured metapopulation model within a stochastic environment.
Smith, Andrew G
2017-09-01
Populations often exist, either by choice or by external pressure, in a fragmented way, referred to as a metapopulation. Typically, the dynamics accounted for within metapopulation models are assumed to be static. For example, patch occupancy models often assume that the colonisation and extinction rates do not change, while spatially structured models often assume that the rates of births, deaths and migrations do not depend on time. While some progress has been made when these dynamics are changing deterministically, less is known when the changes are stochastic. It can be quite common that the environment a population inhabits determines how these dynamics change over time. Changes to this environment can have a large impact on the survival probability of a population and such changes will often be stochastic. The typical metapopulation model allows for catastrophes that could eradicate most, if not all, individuals on an entire patch. It is this type of phenomenon that this article addresses. A Markov process is developed that models the number of individuals on each patch within a metapopulation. An approximation for the original model is presented in the form of a piecewise-deterministic Markov process and the approximation is analysed to present conditions for extinction. Copyright © 2017 Elsevier Inc. All rights reserved.
Stochastic dynamical models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik
phytoplankton and benthic vegetation with feedback mechanisms is formulated, and it is demonstrated that bistability can occur for specific parameter settings. When stochastic input and stochastic propagation of the states are applied on the system regime shifts occur more frequently, and the threshold...
Gompertzian stochastic model with delay effect to cervical cancer growth
International Nuclear Information System (INIS)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-01-01
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits
Gompertzian stochastic model with delay effect to cervical cancer growth
Energy Technology Data Exchange (ETDEWEB)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor and UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-02-03
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Comments on the use of stochastic processes in the field of the ionizing radiations
International Nuclear Information System (INIS)
Alvarez Romero, Jose T.
2008-01-01
Stochastic process is the name given to a time dependent random process, unfortunately, its time dependence is not always clearly emphasized. In fact, such dependence is not unequivocally stated in the different disciplines of radiation physics, radiobiology or in radiation protection. This is the cause of some conceptual confusion when interpreting relationships between quantities is analyzed, e.g.: imparted energy vs. absorbed dose, stochastic vs. deterministic biological effects; or in radiation protection models, whether: linear or quadratic, relative or absolute. Most of these relationships are associated to stochastic phenomena, and they carry a time dependence that requires clarification. To mention some examples, in radiation physics: the absorbed dose is a non stochastic quantity resulting from averaging a stochastic one namely, the imparted energy, over a representative ensemble via an operation analogous to the Gibbs-Einstein algorithm. On the other hand stochastic quantities require specialized mathematical techniques of stochastic processes to handle them. These refinements are unfortunately ignored in the reports of ICRU 33 and 60. Essentially, a problem to be solved is to establish a clear relationship between micro or mesoscopic stochastic quantities and their macroscopic counterparts, these latter ones possibly being time dependent or not. This is the main objective of microdosimetry. Another problem is to describe phenomena such as electronic equilibrium which is nothing else than a stationary state thus exhibiting no time dependence. Still a different question is the interpretation of radioactive decay as a stochastic process of the Poisson and Markov type. In radiobiology a basic problem is the study of biological stochastic phenomena is to determine the characteristics and structure of those time dependent probabilistic functions allowing the quantification of macroscopic biological manifestations, such as carcinogenesis or genetic effects
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.
A stochastic model for early placental development.
Cotter, Simon L
2014-08-01
In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational-age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely understood and are difficult to study in vivo. In this paper, we model the early development of the human placenta, based on the hypothesis that this is driven by a chemoattractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that disruption of spiral arteries can exert profound effects on placental shape, particularly if this is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, predisposing to pregnancy complications. Through statistical analysis of model placentas, we are able to characterize the probability that a given placenta grew in a disrupted environment, and even able to distinguish between different disruptions.
Stochastic modelling of two-phase flows including phase change
International Nuclear Information System (INIS)
Hurisse, O.; Minier, J.P.
2011-01-01
Stochastic modelling has already been developed and applied for single-phase flows and incompressible two-phase flows. In this article, we propose an extension of this modelling approach to two-phase flows including phase change (e.g. for steam-water flows). Two aspects are emphasised: a stochastic model accounting for phase transition and a modelling constraint which arises from volume conservation. To illustrate the whole approach, some remarks are eventually proposed for two-fluid models. (authors)
Expectation propagation for continuous time stochastic processes
International Nuclear Information System (INIS)
Cseke, Botond; Schnoerr, David; Sanguinetti, Guido; Opper, Manfred
2016-01-01
We consider the inverse problem of reconstructing the posterior measure over the trajectories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference, giving rise to an expectation propagation type algorithm. For non-linear diffusion processes, this is achieved by leveraging moment closure approximations. We then show how the approximation can be extended to a wide class of discrete-state Markov jump processes by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems. (paper)
Stochastic Higher Spin Vertex Models on the Line
Corwin, Ivan; Petrov, Leonid
2016-04-01
We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain Markov dualities. Using this, for the systems started in step initial data, we write down nested contour integral formulas for moments and Fredholm determinant formulas for Laplace-type transforms. Taking various choices or limits of parameters, this family degenerates to many of the known exactly solvable models in the Kardar-Parisi-Zhang universality class, as well as leads to many new examples of such models. In particular, asymmetric simple exclusion process, the stochastic six-vertex model, q-totally asymmetric simple exclusion process and various directed polymer models all arise in this manner. Our systems are constructed from stochastic versions of the R-matrix related to the six-vertex model. One of the key tools used here is the fusion of R-matrices and we provide a probabilistic proof of this procedure.
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.
The stochastic resonance for the incidence function model of metapopulation
Li, Jiang-Cheng; Dong, Zhi-Wei; Zhou, Ruo-Wei; Li, Yun-Xian; Qian, Zhen-Wei
2017-06-01
A stochastic model with endogenous and exogenous periodicities is proposed in this paper on the basis of metapopulation dynamics to model the crop yield losses due to pests and diseases. The rationale is that crop yield losses occur because the physiology of the growing crop is negatively affected by pests and diseases in a dynamic way over time as crop both grows and develops. Metapopulation dynamics can thus be used to model the resultant crop yield losses. The stochastic metapopulation process is described by using the Simplified Incidence Function model (IFM). Compared to the original IFMs, endogenous and exogenous periodicities are considered in the proposed model to handle the cyclical patterns observed in pest infestations, diseases epidemics, and exogenous affecting factors such as temperature and rainfalls. Agricultural loss data in China are used to fit the proposed model. Experimental results demonstrate that: (1) Model with endogenous and exogenous periodicities is a better fit; (2) When the internal system fluctuations and external environmental fluctuations are negatively correlated, EIL or the cost of loss is monotonically increasing; when the internal system fluctuations and external environmental fluctuations are positively correlated, an outbreak of pests and diseases might occur; (3) If the internal system fluctuations and external environmental fluctuations are positively correlated, an optimal patch size can be identified which will greatly weaken the effects of external environmental influence and hence inhibit pest infestations and disease epidemics.
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
A probabilistic graphical model based stochastic input model construction
International Nuclear Information System (INIS)
Wan, Jiang; Zabaras, Nicholas
2014-01-01
Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media
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...
Characterizing economic trends by Bayesian stochastic model specification search
DEFF Research Database (Denmark)
Grassi, Stefano; Proietti, Tommaso
on whether their parameters are fixed or evolutive. Stochastic model specification is carried out to discriminate two alternative hypotheses concerning the generation of trends: the trend-stationary hypothesis, on the one hand, for which the trend is a deterministic function of time and the short run...... dynamics are represented by a stationary autoregressive process; the difference-stationary hypothesis, on the other, according to which the trend results from the cumulation of the effects of random disturbances. We illustrate the methodology for a set of U.S. macroeconomic time series, which includes...
Economic-oriented stochastic optimization in advanced process control of chemical processes.
Dobos, László; Király, András; Abonyi, János
2012-01-01
Finding the optimal operating region of chemical processes is an inevitable step toward improving economic performance. Usually the optimal operating region is situated close to process constraints related to product quality or process safety requirements. Higher profit can be realized only by assuring a relatively low frequency of violation of these constraints. A multilevel stochastic optimization framework is proposed to determine the optimal setpoint values of control loops with respect to predetermined risk levels, uncertainties, and costs of violation of process constraints. The proposed framework is realized as direct search-type optimization of Monte-Carlo simulation of the controlled process. The concept is illustrated throughout by a well-known benchmark problem related to the control of a linear dynamical system and the model predictive control of a more complex nonlinear polymerization process.
The Stochastic stability of a Logistic model with Poisson white noise
International Nuclear Information System (INIS)
Duan Dong-Hai; Xu Wei; Zhou Bing-Chang; Su Jun
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 Itô 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. (general)
The Stochastic stability of a Logistic model with Poisson white noise
Duan, Dong-Hai; Xu, Wei; Su, Jun; Zhou, Bing-Chang
2011-03-01
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 Itô 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. Project supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10932009).
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 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.
Rifhat, Ramziya; Wang, Lei; Teng, Zhidong
2017-09-01
In this paper, we investigate the dynamics of a class of periodic stochastic SIS epidemic models with general nonlinear incidence f(S , I) . Some sufficient conditions on the permanence in the mean and extinction of positive solutions with probability one are established. By using the Khasminskii's boundary periodic Markov processes, the existence of stochastic nontrivial periodic solution for the models is also obtained. The numerical simulations are given to illustrate the main theoretical results and some interesting conjectures are presented.
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.
Stochastic modeling of wetland-groundwater systems
Bertassello, Leonardo Enrico; Rao, P. Suresh C.; Park, Jeryang; Jawitz, James W.; Botter, Gianluca
2018-02-01
Modeling and data analyses were used in this study to examine the temporal hydrological variability in geographically isolated wetlands (GIWs), as influenced by hydrologic connectivity to shallow groundwater, wetland bathymetry, and subject to stochastic hydro-climatic forcing. We examined the general case of GIWs coupled to shallow groundwater through exfiltration or infiltration across wetland bottom. We also examined limiting case with the wetland stage as the local expression of the shallow groundwater. We derive analytical expressions for the steady-state probability density functions (pdfs) for wetland water storage and stage using few, scaled, physically-based parameters. In addition, we analyze the hydrologic crossing time properties of wetland stage, and the dependence of the mean hydroperiod on climatic and wetland morphologic attributes. Our analyses show that it is crucial to account for shallow groundwater connectivity to fully understand the hydrologic dynamics in wetlands. The application of the model to two different case studies in Florida, jointly with a detailed sensitivity analysis, allowed us to identify the main drivers of hydrologic dynamics in GIWs under different climate and morphologic conditions.
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
Estimation of some stochastic models used in reliability engineering
International Nuclear Information System (INIS)
Huovinen, T.
1989-04-01
The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a beta-binomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gamma-poisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilizing point processes. Here we consider the statistical analysis of non-homogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method
Stochastic Watershed Models for Risk Based Decision Making
Vogel, R. M.
2017-12-01
Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation
Model selection for integrated pest management with stochasticity.
Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel
2018-04-07
In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model. Copyright © 2017 Elsevier Ltd. All rights reserved.
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...
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.
Some Remarks on Stochastic Versions of the Ramsey Growth Model
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2012-01-01
Roč. 19, č. 29 (2012), s. 139-152 ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/10/0956; GA ČR GAP402/11/0150 Institutional support: RVO:67985556 Keywords : Economic dynamics * Ramsey growth model with disturbance * stochastic dynamic programming * multistage stochastic programs Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/sladky-some remarks on stochastic versions of the ramsey growth model.pdf
Asymptotic and transient analysis of stochastic core ecosystem models
Directory of Open Access Journals (Sweden)
Thomas C. Gard
2000-07-01
Full Text Available General results on ultimate boundedness and exit probability estimates for stochastic differential equations are applied to investigate asymptotic and transient properties of models of plankton-fish dynamics in uncertain environments
Stochastic Modeling of the Persistence of HIV: Early Population Dynamics
2013-05-10
move about. Mathematically, this process was described first by Norbert Wiener , after whom the process is named. We abbreviate the Wiener process W...stochastic process is Brownian motion, which is also known as the Wiener process. Originally used to describe the motion of particles suspended within a
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. © 2015. Published by The Company of Biologists Ltd.
Modeling energy price dynamics: GARCH versus stochastic volatility
International Nuclear Information System (INIS)
Chan, Joshua C.C.; Grant, Angelia L.
2016-01-01
We compare a number of GARCH and stochastic volatility (SV) models using nine series of oil, petroleum product and natural gas prices in a formal Bayesian model comparison exercise. The competing models include the standard models of GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, and t distributed and moving average innovations. We find that: (1) SV models generally compare favorably to their GARCH counterparts; (2) the jump component and t distributed innovations substantially improve the performance of the standard GARCH, but are unimportant for the SV model; (3) the volatility feedback channel seems to be superfluous; (4) the moving average component markedly improves the fit of both GARCH and SV models; and (5) the leverage effect is important for modeling crude oil prices—West Texas Intermediate and Brent—but not for other energy prices. Overall, the SV model with moving average innovations is the best model for all nine series. - Highlights: • We compare a variety of GARCH and SV models for fitting nine series of energy prices. • We find that SV models generally compare favorably to their GARCH counterparts. • The SV model with moving average innovations is the best model for all nine series.
On the Stochastic Dynamics of a Social Epidemics Model
Directory of Open Access Journals (Sweden)
Xun-Yang Wang
2017-01-01
Full Text Available Alcohol abuse is a major social problem, which has caused a lot of damages or hidden dangers to the individual and the society. In this paper, with random factors of alcoholism considered in mortality rate of compartment populations, we formulate a stochastic alcoholism model according to compartment theory of infectious disease. Based on this model, we investigate the long-term stochastic dynamics behaviors of two equilibria of the corresponding deterministic model and point out the effect of random disturbance on the stability of the system. We find that when R0≤1, we get the estimation between the trajectory of stochastic system and E0=(Π/μs,0,0,0 in the average in time with respect to the disturbance intensity, while when R0>1, stochastic system is ergodic and has the unique stationary distribution. Finally, we carry out numerical simulations to support the corresponding theoretical results.
Bouchaud, Jean-Philippe; Sornette, Didier
1994-01-01
The ability to price risks and devise optimal investment strategies in thé présence of an uncertain "random" market is thé cornerstone of modern finance theory. We first consider thé simplest such problem of a so-called "European call option" initially solved by Black and Scholes using Ito stochastic calculus for markets modelled by a log-Brownien stochastic process. A simple and powerful formalism is presented which allows us to generalize thé analysis to a large class of stochastic processe...
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.
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.
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.
Using an atmospheric turbulence model for the stochastic model of geodetic VLBI data analysis
Halsig, Sebastian; Artz, Thomas; Iddink, Andreas; Nothnagel, Axel
2016-06-01
Space-geodetic techniques at radio wavelength, such as global navigation satellite systems and very long baseline interferometry (VLBI), suffer from refractivity of the Earth's atmosphere. These highly dynamic processes, particularly refractivity variations in the neutral atmosphere, contribute considerably to the error budget of these space-geodetic techniques. Here, microscale fluctuations in refractivity lead to elevation-dependent uncertainties and induce physical correlations between the observations. However, up to now such correlations are not considered routinely in the stochastic model of space-geodetic observations, which leads to very optimistic standard deviations of the derived target parameters, such as Earth orientation parameters and station positions. In this study, the standard stochastic model of VLBI observations, which only includes, almost exclusively, the uncertainties from the VLBI correlation process, is now augmented by a variance-covariance matrix derived from an atmospheric turbulence model. Thus, atmospheric refractivity fluctuations in space and time can be quantified. One of the main objectives is to realize a suitable stochastic model of VLBI observations in an operational way. In order to validate the new approach, the turbulence model is applied to several VLBI observation campaigns consisting of different network geometries leading the path for the next-generation VLBI campaigns. It is shown that the stochastic model of VLBI observations can be improved by using high-frequency atmospheric variations and, thus, refining the stochastic model leads to far more realistic standard deviations of the target parameters. The baseline length repeatabilities as a general measure of accuracy of baseline length determinations improve for the turbulence-based solution. Further, this method is well suited for routine VLBI data analysis with limited computational costs.
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.
Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings
Cunha, Americo; Soize, Christian; Sampaio, Rubens
2015-11-01
This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.
A stochastic model for speciation by mating preferences.
Coron, Camille; Costa, Manon; Leman, Hélène; Smadi, Charline
2018-05-01
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the carrying capacity. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations.
Stochastic dynamic programming model for optimal resource ...
Indian Academy of Sciences (India)
M Bhuvaneswari
2018-04-11
Apr 11, 2018 ... containers, doctors, nurses, cash and stocks. Similarly, the uncertainty may have different characterizations in these applications. An approximate stochastic dynamic programming (SDP) [3] allows nodes with a number of possible actions with clear strategies for devising an effective decision on optimal ...
Composed particle model in stochastic electrodynamics
International Nuclear Information System (INIS)
Brunini, S.A.
1985-01-01
We analyse the statistical properties of the non-relativistic motion of a particle that has two constituents having finite nasses and charges. The main interaction is in contact with thermal and zero point radiation of Stochastic Electrodynamics. (M.W.O.) [pt
A complementarity model for solving stochastic natural gas market equilibria
International Nuclear Information System (INIS)
Zhuang Jifang; Gabriel, Steven A.
2008-01-01
This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems
A complementarity model for solving stochastic natural gas market equilibria
International Nuclear Information System (INIS)
Jifang Zhuang; Gabriel, S.A.
2008-01-01
This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems. (author)
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 bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
Directory of Open Access Journals (Sweden)
Elston Timothy C
2004-03-01
Full Text Available Abstract Background Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. Results We have developed the software package Biochemical Network Stochastic Simulator (BioNetS for efficientlyand accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solvesthe appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. Conclusions We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.
Simulation of the stochastic wave loads using a physical modeling approach
DEFF Research Database (Denmark)
Liu, W.F.; Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2013-01-01
In analyzing stochastic dynamic systems, analysis of the system uncertainty due to randomness in the loads plays a crucial role. Typically time series of the stochastic loads are simulated using traditional random phase method. This approach combined with fast Fourier transform algorithm makes...... an efficient way of simulating realizations of the stochastic load processes. However it requires many random variables, i.e. in the order of magnitude of 1000, to be included in the load model. Unfortunately having too many random variables in the problem makes considerable difficulties in analyzing system...... reliability or its uncertainty. Moreover applicability of the probability density evolution method on engineering problems faces critical difficulties when the system embeds too many random variables. Hence it is useful to devise a method which can make realization of the stochastic load processes with low...
ParPor: Particles in Pores. Stochastic Modeling of Polydisperse Transport
DEFF Research Database (Denmark)
Yuan, Hao
2010-01-01
Liquid flow containing particles in the different types of porous media appear in a large variety of practically important industrial and natural processes. The project aims at developing a stochastic model for the deep bed filtration process in which the polydisperse suspension flow in the polyd......Liquid flow containing particles in the different types of porous media appear in a large variety of practically important industrial and natural processes. The project aims at developing a stochastic model for the deep bed filtration process in which the polydisperse suspension flow...... in the polydisperse porous media. Instead of the traditional parabolic Advection-Dispersion Equation (ADE) the novel elliptic PDE based on the Continuous Time Random Walk is adopted for the particle size kinetics. The pore kinetics is either described by the stochastic size exclusion mechanism or the incomplete pore...... of the porous media and convection acceleration of the flow are observed from the modeling results which agree with the general experimental observation....
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.
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
Analysis of stochastic model for nonlinear volcanic dynamics
Alexandrov, D. V.; Bashkirtseva, I. A.; Ryashko, L. B.
2015-01-01
Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al.~(2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for a solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories ar...
Analysis of stochastic model for non-linear volcanic dynamics
D. Alexandrov; I. Bashkirtseva; L. Ryashko
2014-01-01
Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random ...
A Stochastic Continuous Time Model for Microgrid Energy Management
Heymann, Benjamin; Frédéric Bonnans, J; Silva, Francisco; Jimenez, Guillermo
2016-01-01
International audience; We propose a novel stochastic control formulation for the microgrid energy management problem and extend previous works on continuous time rolling horizon strategy to uncertain demand. We modelize the demand dynamics with a stochastic differential equation. We decompose this dynamics into three terms: an average drift, a time-dependent mean-reversion term and a Brownian noise. We use BOCOPHJB for the numerical simulations. This optimal control toolbox implements a semi...
Analysis of dynamic regimes in stochastically forced Kaldor model
International Nuclear Information System (INIS)
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-01-01
We consider the business cycle Kaldor model forced by random noise. Detailed parametric analysis of deterministic system is carried out and zones of coexisting stable equilibrium and stable limit cycle are found. Noise-induced transitions between these attractors are studied using stochastic sensitivity function technique and confidence domains method. Critical values of noise intensity corresponding to noise-induced transitions “equilibrium → cycle” and “cycle → equilibrium” are estimated. Dominants in combined stochastic regimes are discussed.
Introduction to stochastic models in biology
DEFF Research Database (Denmark)
Ditlevsen, Susanne; Samson, Adeline
2013-01-01
This chapter is concerned with continuous time processes, which are often modeled as a system of ordinary differential equations (ODEs). These models assume that the observed dynamics are driven exclusively by internal, deterministic mechanisms. However, real biological systems will always be exp...
On a Stochastic Model in Insurance
Indian Academy of Sciences (India)
2. Life insurance/pension insurance models are gen- erally described in terms of continuous time Markov processes with state space having only a finite number of elements; at least one state is absorbing, and cer- tain transitions may be disallowed. For example, in the simplest life insurance model there are only two states,.
Stochastic modeling of interannual variation of hydrologic variables
Dralle, David; Karst, Nathaniel; Müller, Marc; Vico, Giulia; Thompson, Sally E.
2017-07-01
Quantifying the interannual variability of hydrologic variables (such as annual flow volumes, and solute or sediment loads) is a central challenge in hydrologic modeling. Annual or seasonal hydrologic variables are themselves the integral of instantaneous variations and can be well approximated as an aggregate sum of the daily variable. Process-based, probabilistic techniques are available to describe the stochastic structure of daily flow, yet estimating interannual variations in the corresponding aggregated variable requires consideration of the autocorrelation structure of the flow time series. Here we present a method based on a probabilistic streamflow description to obtain the interannual variability of flow-derived variables. The results provide insight into the mechanistic genesis of interannual variability of hydrologic processes. Such clarification can assist in the characterization of ecosystem risk and uncertainty in water resources management. We demonstrate two applications, one quantifying seasonal flow variability and the other quantifying net suspended sediment export.
Stochastic hybrid model of spontaneous dendritic NMDA spikes
International Nuclear Information System (INIS)
Bressloff, Paul C; Newby, Jay M
2014-01-01
Following recent advances in imaging techniques and methods of dendritic stimulation, active voltage spikes have been observed in thin dendritic branches of excitatory pyramidal neurons, where the majority of synapses occur. The generation of these dendritic spikes involves both Na + ion channels and M-methyl-D-aspartate receptor (NMDAR) channels. During strong stimulation of a thin dendrite, the resulting high levels of glutamate, the main excitatory neurotransmitter in the central nervous system and an NMDA agonist, modify the current-voltage (I–V) characteristics of an NMDAR so that it behaves like a voltage-gated Na + channel. Hence, the NMDARs can fire a regenerative dendritic spike, just as Na + channels support the initiation of an action potential following membrane depolarization. However, the duration of the dendritic spike is of the order 100 ms rather than 1 ms, since it involves slow unbinding of glutamate from NMDARs rather than activation of hyperpolarizing K + channels. It has been suggested that dendritic NMDA spikes may play an important role in dendritic computations and provide a cellular substrate for short-term memory. In this paper, we consider a stochastic, conductance-based model of dendritic NMDA spikes, in which the noise originates from the stochastic opening and closing of a finite number of Na + and NMDA receptor ion channels. The resulting model takes the form of a stochastic hybrid system, in which membrane voltage evolves according to a piecewise deterministic dynamics that is coupled to a jump Markov process describing the opening and closing of the ion channels. We formulate the noise-induced initiation and termination of a dendritic spike in terms of a first-passage time problem, under the assumption that glutamate unbinding is negligible, which we then solve using a combination of WKB methods and singular perturbation theory. Using a stochastic phase-plane analysis we then extend our analysis to take proper account of the
Using stochastic models to incorporate spatial and temporal variability [Exercise 14
Carolyn Hull Sieg; Rudy M. King; Fred Van Dyke
2003-01-01
To this point, our analysis of population processes and viability in the western prairie fringed orchid has used only deterministic models. In this exercise, we conduct a similar analysis, using a stochastic model instead. This distinction is of great importance to population biology in general and to conservation biology in particular. In deterministic models,...
Stochastic approach to pitting-corrosion-extreme modelling in low-carbon steel
Energy Technology Data Exchange (ETDEWEB)
Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado 10400, La Habana (Cuba); Caleyo, F. [Departamento de Ingenieria Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Rivas, D.; Hallen, J.M. [Departamento de Ingenieria Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)
2010-03-15
A stochastic model previously developed by the authors using Markov chains has been improved in the light of new experimental evidence. The new model has been successfully applied to reproduce the time evolution of extreme pitting corrosion depths in low-carbon steel. The model is shown to provide a better physical understanding of the pitting process.
Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models
International Nuclear Information System (INIS)
Eyink, Gregory L.
2009-01-01
We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.
Modeling ion channel dynamics through reflected stochastic differential equations.
Dangerfield, Ciara E; Kay, David; Burrage, Kevin
2012-05-01
Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks.
Conditional Stochastic Processes Applied to Wave Load Predictions
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
2015-01-01
with an application where measured wave responses are used to predict the future variation in the responses within the next 5-30 seconds. The main part of the article is devoted to the application of the First Order Reliability Method for derivation of critical wave episodes for different nonlinear wave......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 the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation...
Stochastic models to simulate paratuberculosis in dairy herds
DEFF Research Database (Denmark)
Nielsen, Søren Saxmose; Weber, M.F.; Kudahl, Anne Margrethe Braad
2011-01-01
Stochastic simulation models are widely accepted as a means of assessing the impact of changes in daily management and the control of different diseases, such as paratuberculosis, in dairy herds. This paper summarises and discusses the assumptions of four stochastic simulation models and their use...... the models are somewhat different in their underlying principles and do put slightly different values on the different strategies, their overall findings are similar. Therefore, simulation models may be useful in planning paratuberculosis strategies in dairy herds, although as with all models caution...
Deterministic and stochastic CTMC models from Zika disease transmission
Zevika, Mona; Soewono, Edy
2018-03-01
Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.
A nested multisite daily rainfall stochastic generation model
Srikanthan, Ratnasingham; Pegram, Geoffrey G. S.
2009-06-01
SummaryThis paper describes a nested multisite daily rainfall generation model which preserves the statistics at daily, monthly and annual levels of aggregation. A multisite two-part daily model is nested in multisite monthly, then annual models. A multivariate set of fourth order Markov chains is used to model the daily occurrence of rainfall; the daily spatial correlation in the occurrence process is handled by using suitably correlated uniformly distributed variates via a Normal Scores Transform (NST) obtained from a set of matched multinormal pseudo-random variates, following Wilks [Wilks, D.S., 1998. Multisite generalisation of a daily stochastic precipitation generation model. Journal of Hydrology 210, 178-191]; we call it a hidden covariance model. A spatially correlated two parameter gamma distribution is used to obtain the rainfall depths; these values are also correlated via a specially matched hidden multinormal process. For nesting, the generated daily rainfall sequences at all the sites are aggregated to monthly rainfall values and these values are modified by a set of lag-1 autoregressive multisite monthly rainfall models. The modified monthly rainfall values are aggregated to annual rainfall and these are then modified by a lag-1 autoregressive multisite annual model. This nesting process ensures that the daily, monthly and annual means and covariances are preserved. The model was applied to a region with 30 rainfall sites, one of the five sets reported by Srikanthan [Srikanthan, R., 2005. Stochastic Generation of Daily Rainfall Data at a Number of Sites. Technical Report 05/7, CRC for Catchment Hydrology. Monash University, 66p]. A comparison of the historical and generated statistics shows that the model preserves all the important characteristics of rainfall at the daily, monthly and annual time scales, including the spatial structure. There are some outstanding features that need to be improved: depths of rainfall on isolated wet days and
On impulsive integrated pest management models with stochastic effects.
Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel
2015-01-01
We extend existing impulsive differential equation models for integrated pest management (IPM) by including stage structure for both predator and prey as well as by adding stochastic elements in the birth rate of the prey. Based on our model, we propose an approach that incorporates various competing stochastic components. This approach enables us to select a model with optimally determined weights for maximum accuracy and precision in parameter estimation. This is significant in the case of IPM because the proposed model accommodates varying unknown environmental and climatic conditions, which affect the resources needed for pest eradication.
Stochastic evolutions of dynamic traffic flow modeling and applications
Chen, Xiqun (Michael); Shi, Qixin
2015-01-01
This book reveals the underlying mechanisms of complexity and stochastic evolutions of traffic flows. Using Eulerian and Lagrangian measurements, the authors propose lognormal headway/spacing/velocity distributions and subsequently develop a Markov car-following model to describe drivers’ random choices concerning headways/spacings, putting forward a stochastic fundamental diagram model for wide scattering flow-density points. In the context of highway onramp bottlenecks, the authors present a traffic flow breakdown probability model and spatial-temporal queuing model to improve the stability and reliability of road traffic flows. This book is intended for researchers and graduate students in the fields of transportation engineering and civil engineering.
INFERENCE AND SENSITIVITY IN STOCHASTIC WIND POWER FORECAST MODELS.
Elkantassi, Soumaya
2017-10-03
Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.
Stochastic description of heterogeneities of permeability within groundwater flow models
International Nuclear Information System (INIS)
Cacas, M.C.; Lachassagne, P.; Ledoux, E.; Marsily, G. de
1991-01-01
In order to model radionuclide migration in the geosphere realistically at the field scale, the hydrogeologist needs to be able to simulate groundwater flow in heterogeneous media. Heterogeneity of the medium can be described using a stochastic approach, that affects the way in which a flow model is formulated. In this paper, we discuss the problems that we have encountered in modelling both continuous and fractured media. The stochastic approach leads to a methodology that enables local measurements of permeability to be integrated into a model which gives a good prediction of groundwater flow on a regional scale. 5 Figs.; 8 Refs
Advanced Stochastic Modeling of Railway Track Irregularities
Directory of Open Access Journals (Sweden)
Mengyi Zhu
2013-01-01
Full Text Available As an important interference source of railway vibration, track irregularity is studied in this paper. It is presented that irregularities in the vertical profile and alignment can be modeled as a Gaussian random process. The power spectral density (PSD of the irregularity is calculated and discussed. By analyzing the model, level-crossing properties as well as peak statistics are studied and compared with the observed data.
Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.
García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G
2017-08-01
The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.
Stochastic Approximation Methods for Latent Regression Item Response Models
von Davier, Matthias; Sinharay, Sandip
2010-01-01
This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates…
A stochastic dynamic programming model for stream water quality ...
Indian Academy of Sciences (India)
This paper deals with development of a seasonal fraction-removal policy model for waste load allocation in streams addressing uncertainties due to randomness and fuzziness. A stochastic dynamic programming (SDP) model is developed to arrive at the steady-state seasonal fraction-removal policy. A fuzzy decision model ...
Effects of Stochastic Traffic Flow Model on Expected System Performance
2012-12-01
feasible. 2.2.2 Brownian Bridge Stochastic Path Model Like the linear model, the Brownian bridge ( Karlin and Taylor 1981) model uses the idea of...IEEE Computer Vision and Pattern Recog- nition Workshop, Piscataway, New Jersey: Institute of Electrical and Electronics Engineers, Inc. Karlin , S
Stochastic models for some meteorological outcomes in Niger Delta ...
African Journals Online (AJOL)
In this paper, stochastic models based on autoregressive integrated moving average models of various orders and its seasonalized versions are presented, with a view to identifying the optimal model for some meteorological outcomes in some cities in Niger Delta region of Nigeria, using Normalized Bayesian Information ...
On a Versatile Stochastic Growth Model
Directory of Open Access Journals (Sweden)
Samiur Arif
2012-06-01
Full Text Available Growth phenomena are ubiquitous and pervasive not only in biology and the medical sciences, but also in economics, marketing and the computer and social sciences. We introduce a three-parameter version of the classic pure-birth process growth model when suitably instantiated, can be used to model growth phenomena in many seemingly unrelated application domains. We point out that the model is computationally attractive since it admits of conceptually simple, closed form solutions for the time-dependent probabilities.
Stochastic modeling of the cover effect and bedrock erosion
Turowski, Jens M.
2009-03-01
Several important fluvial bedrock erosion processes are driven by the impact of bed load particles. Bed load transport rates fluctuate strongly in both nature and experiment, and stochastic models of the transport processes have been put forward to describe this behavior. In this paper I adapt a model based on a Markov chain formulation to derive probability distributions for bed load transport rate over a rock bed only partly covered by sediment. I propose a way to calculate the probability distribution of bed cover for given sediment supply using a combinatoric model and combine the two curves to calculate probability distributions for bed cover and erosion rate at constant hydraulics. In the proposed model, mean bed cover is an exponentially declining function of the number of particles in the control volume. The model describes recently published experimental data well, but at the moment it is not possible to finally discriminate between the exponential and the previously proposed linear model formulation. Distributions of erosion rate are fairly broad functions slightly skewed toward high erosion rates.
Stochastic modelling of dynamical systems in biology
Pellin, Danilo
2017-01-01
In this thesis two relevant biological problems will be addressed from a statistical modelling perspective. The first regards the study of hematopoiesis, a still not well understood biological process rarely observable in humans due to technical and ethical reasons. Hematopoiesis is responsible for
Pricing foreign equity option under stochastic volatility tempered stable Lévy processes
Gong, Xiaoli; Zhuang, Xintian
2017-10-01
Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.
Yang, Xin; Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan
2016-01-01
This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems.
Stochastic Energy Deployment System (SEDS) World Oil Model (WOM)
Energy Technology Data Exchange (ETDEWEB)
2009-08-07
The function of the World Oil Market Model (WOMM) is to calculate a world oil price. SEDS will set start and end dates for the forecast period, and a time increment (assumed to be 1 year in the initial version). The WOMM will then randomly select an Annual Energy Outlook (AEO) oil price case and calibrate itself to that case. As it steps through each year, the WOMM will generate a stochastic supply shock to OPEC output and accept a new estimate of U.S. petroleum demand from SEDS. The WOMM will then calculate a new oil market equilibrium for the current year. The world oil price at the new equilibrium will be sent back to SEDS. When the end year is reached, the process will begin again with the selection of a new AEO forecast. Iterations over forecasts will continue until SEDS has completed all its simulation runs.
Maximum caliber inference and the stochastic Ising model
Cafaro, Carlo; Ali, Sean Alan
2016-11-01
We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.
Stochastic Modeling Approach to the Incubation Time of Prionic Diseases
Ferreira, A. S.; da Silva, M. A.; Cressoni, J. C.
2003-05-01
Transmissible spongiform encephalopathies are neurodegenerative diseases for which prions are the attributed pathogenic agents. A widely accepted theory assumes that prion replication is due to a direct interaction between the pathologic (PrPSc) form and the host-encoded (PrPC) conformation, in a kind of autocatalytic process. Here we show that the overall features of the incubation time of prion diseases are readily obtained if the prion reaction is described by a simple mean-field model. An analytical expression for the incubation time distribution then follows by associating the rate constant to a stochastic variable log normally distributed. The incubation time distribution is then also shown to be log normal and fits the observed BSE (bovine spongiform encephalopathy) data very well. Computer simulation results also yield the correct BSE incubation time distribution at low PrPC densities.
Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Kiem, A.; Nadeeka, P. M.
2016-12-01
One of the key objectives of stochastic rainfall modelling is to capture the full variability of climate system for future drought and flood risk assessment. However, it is not clear how well these models can capture the future climate variability when they are calibrated to Global/Regional Climate Model data (GCM/RCM) as these datasets are usually available for very short future period/s (e.g. 20 years). This study has assessed the ability of two stochastic daily rainfall models to capture climate variability by calibrating them to a dynamically downscaled RCM dataset in an east Australian catchment for 1990-2010, 2020-2040, and 2060-2080 epochs. The two stochastic models are: (1) a hierarchical Markov Chain (MC) model, which we developed in a previous study and (2) a semi-parametric MC model developed by Mehrotra and Sharma (2007). Our hierarchical model uses stochastic parameters of MC and Gamma distribution, while the semi-parametric model uses a modified MC process with memory of past periods and kernel density estimation. This study has generated multiple realizations of rainfall series by using parameters of each model calibrated to the RCM dataset for each epoch. The generated rainfall series are used to generate synthetic streamflow by using a SimHyd hydrology model. Assessing the synthetic rainfall and streamflow series, this study has found that both stochastic models can incorporate a range of variability in rainfall as well as streamflow generation for both current and future periods. However, the hierarchical model tends to overestimate the multiyear variability of wet spell lengths (therefore, is less likely to simulate long periods of drought and flood), while the semi-parametric model tends to overestimate the mean annual rainfall depths and streamflow volumes (hence, simulated droughts are likely to be less severe). Sensitivity of these limitations of both stochastic models in terms of future drought and flood risk assessment will be discussed.
Dini-Andreote, Francisco; Stegen, James C; van Elsas, Jan Dirk; Salles, Joana Falcão
2015-03-17
Ecological succession and the balance between stochastic and deterministic processes are two major themes within microbial ecology, but these conceptual domains have mostly developed independent of each other. Here we provide a framework that integrates shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. Synthesizing previous work, we devised a conceptual model that links ecosystem development to alternative hypotheses related to shifts in ecological assembly processes. Conceptual model hypotheses were tested by coupling spatiotemporal data on soil bacterial communities with environmental conditions in a salt marsh chronosequence spanning 105 years of succession. Analyses within successional stages showed community composition to be initially governed by stochasticity, but as succession proceeded, there was a progressive increase in deterministic selection correlated with increasing sodium concentration. Analyses of community turnover among successional stages--which provide a larger spatiotemporal scale relative to within stage analyses--revealed that changes in the concentration of soil organic matter were the main predictor of the type and relative influence of determinism. Taken together, these results suggest scale-dependency in the mechanisms underlying selection. To better understand mechanisms governing these patterns, we developed an ecological simulation model that revealed how changes in selective environments cause shifts in the stochastic/deterministic balance. Finally, we propose an extended--and experimentally testable--conceptual model integrating ecological assembly processes with primary and secondary succession. This framework provides a priori hypotheses for future experiments, thereby facilitating a systematic approach to understand assembly and succession in microbial communities across ecosystems.
Deterministic and stochastic models for middle east respiratory syndrome (MERS)
Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning
2018-03-01
World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.
A stochastic model for intermittent search strategies
International Nuclear Information System (INIS)
Benichou, O; Coppey, M; Moreau, M; Suet, P H; Voituriez, R
2005-01-01
It is often necessary, in scientific or everyday life problems, to find a randomly hidden target. What is then the optimal strategy to reach it as rapidly as possible? In this article, we develop a stochastic theory for intermittent search behaviours, which are often observed: the searcher alternates phases of intensive search and slow motion with fast displacements. The first results of this theory have already been announced recently. Here we provide a detailed presentation of the theory, as well as the full derivation of the results. Furthermore, we explicitly discuss the minimization of the time needed to find the target
Stochastic reduced order models for inverse problems under uncertainty.
Warner, James E; Aquino, Wilkins; Grigoriu, Mircea D
2015-03-01
This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well.
Powering stochastic reliability models by discrete event simulation
DEFF Research Database (Denmark)
Kozine, Igor; Wang, Xiaoyun
2012-01-01
it difficult to find a solution to the problem. The power of modern computers and recent developments in discrete-event simulation (DES) software enable to diminish some of the drawbacks of stochastic models. In this paper we describe the insights we have gained based on using both Markov and DES models...
Dynamic two state stochastic models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Niels Jacob; Madsen, Henrik
2009-01-01
A simple non-linear stochastic two state, discrete-time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the nonlinear functions. The dynamical behavior of the deterministic part of the m......A simple non-linear stochastic two state, discrete-time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the nonlinear functions. The dynamical behavior of the deterministic part...
Modeling the lake eutrophication stochastic ecosystem and the research of its stability.
Wang, Bo; Qi, Qianqian
2018-03-20
In the reality, the lake system will be disturbed by stochastic factors including the external and internal factors. By adding the additive noise and the multiplicative noise to the right-hand sides of the model equation, the additive stochastic model and the multiplicative stochastic model are established respectively in order to reduce model errors induced by the absence of some physical processes. For both the two kinds of stochastic ecosystems, the authors studied the bifurcation characteristics with the FPK equation and the Lyapunov exponent method based on the Stratonovich-Khasminiskii stochastic average principle. Results show that, for the additive stochastic model, when control parameter (i.e, nutrient loading rate) falls into the interval [0.388644, 0.66003825], there exists bistability for the ecosystem and the additive noise intensities cannot make the bifurcation point drift. In the region of the bistability, the external stochastic disturbance which is one of the main triggers causing the lake eutrophication, may make the ecosystem unstable and induce a transition. When control parameter (nutrient loading rate) falls into the interval (0, 0.388644) and (0.66003825, 1.0), there only exists a stable equilibrium state and the additive noise intensity couldn't change it. For the multiplicative stochastic model, there exists more complex bifurcation performance and the multiplicative ecosystem will be broken by the multiplicative noise. Also, the multiplicative noise could reduce the extent of the bistable region, ultimately, the bistable region vanishes for sufficiently large noise. What's more, both the nutrient loading rate and the multiplicative noise will make the ecosystem have a regime shift. On the other hand, for the two kinds of stochastic ecosystems, the authors also discussed the evolution of the ecological variable in detail by using the Four-stage Runge-Kutta method of strong order γ=1.5. The numerical method was found to be
Analyzing a stochastic process driven by Ornstein-Uhlenbeck noise
Lehle, B.; Peinke, J.
2018-01-01
A scalar Langevin-type process X (t ) that is driven by Ornstein-Uhlenbeck noise η (t ) is non-Markovian. However, the joint dynamics of X and η is described by a Markov process in two dimensions. But even though there exists a variety of techniques for the analysis of Markov processes, it is still a challenge to estimate the process parameters solely based on a given time series of X . Such a partially observed 2D process could, e.g., be analyzed in a Bayesian framework using Markov chain Monte Carlo methods. Alternatively, an embedding strategy can be applied, where first the joint dynamics of X and its temporal derivative X ˙ is analyzed. Subsequently, the results can be used to determine the process parameters of X and η . In this paper, we propose a more direct approach that is purely based on the moments of the increments of X , which can be estimated for different time-increments τ from a given time series. From a stochastic Taylor expansion of X , analytic expressions for these moments can be derived, which can be used to estimate the process parameters by a regression strategy.
International Nuclear Information System (INIS)
Laurens, J.M.
1985-01-01
A computer code was written to model food chains in order to estimate the internal and external doses, for stochastic and non-stochastic effects, on humans (adults and infants). Results are given for 67 radionuclides, for unit concentration in water (1 Bq/L) and in atmosphere (1 Bq/m 3 )
Multi-scenario modelling of uncertainty in stochastic chemical systems
International Nuclear Information System (INIS)
Evans, R. David; Ricardez-Sandoval, Luis A.
2014-01-01
Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent on the uncertain input and reaction system. •The model was computationally more efficient than Kinetic Monte Carlo
DEFF Research Database (Denmark)
Ditlevsen, Susanne; Samson, Adeline
2016-01-01
Dynamics of the membrane potential in a single neuron can be studied by estimating biophysical parameters from intracellular recordings. Diffusion processes, given as continuous solutions to stochastic differential equations, are widely applied as models for the neuronal membrane potential evolut...
Interacting Stochastic Processes: From Viciousness to Caging to Force Chains
Xu, Shiliyang
This thesis documents a quest to develop and study several novel interacting stochastic processes. As for the first example, we generalize a system of vicious random walkers in which the only interaction between any two random walkers is that when they intersect, both walkers are annihilated. We define a system of N vicious accelerating walkers with each walker undergoing random acceleration and compute the survival probability distribution for this system. We also define and study a system of N vicious Levy flights in which any two Levy flights crossing one another annihilate each other. The average mean-squared displacement of a Levy flight is not proportional to time, but scales with what is known as the Levy index divided by two. In both cases, vicious accelerating walkers and vicious Levy flights, we are motivated by ultimately generalizing our understanding of Gaussian random matrices via non-Markovian and non-Gaussian extensions respectively. Moreover, inspired by recent experiments on periodically sheared colloids at low densities, we define and investigate several new contact processes, or interacting stochastic processes, with conserved particle number and three-or-more-body interactions. We do so to characterize the periodically sheared colloidal system at higher densities. We find two new dynamical phase transitions between an active phase, where some fraction of the colloids are always being displaced from their position at the beginning and end of each shear cycle, and an inactive phase in which all colloids return to their initial positions at the end of each shear cycle. One of the transitions is discontinuous, while the second, which is due to a caging, or crowding, effect at high densities, appears to be continuous and in a new universality from what is known as conserved directed percolation. The latter transition may have implications for the onset of glassiness in dense, particulate systems. In addition, this thesis also includes analysis of
Reddy, V R; Reddy, T G; Reddy, P Y; Reddy, K R
2003-01-01
An AC modulation technique is described to convert stochastic signal variations into an amplitude variation and its retrieval through Fourier analysis. It is shown that this AC detection of signals of stochastic processes when processed through auto- and cross-correlation techniques improve the signal-to-noise ratio; the correlation techniques serve a similar purpose of frequency and phase filtering as that of phase-sensitive detection. A few model calculations applied to nuclear spectroscopy measurements such as Angular Correlations, Mossbauer spectroscopy and Pulse Height Analysis reveal considerable improvement in the sensitivity of signal detection. Experimental implementation of the technique is presented in terms of amplitude variations of harmonics representing the derivatives of normal spectra. Improved detection sensitivity to spectral variations is shown to be significant. These correlation techniques are general and can be made applicable to all the fields of particle counting where measurements ar...
Stochastic processes and their spectral representations over non-archimedean fields
Ludkovsky, S. V.
2008-01-01
The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic processes controlled by measures with values in $\\bf K$ and in complete topological vector spaces over $\\bf K$ stochastic integrals are investigated. Vector valued measures and integrals in spaces over $\\bf K$ are studied. Theorems about spectral decompositions...
Stochastic lattice model of synaptic membrane protein domains
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A.
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
Stochastic lattice model of synaptic membrane protein domains.
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism
Directory of Open Access Journals (Sweden)
Jian Zhang
2017-01-01
Full Text Available A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.
A measure theoretical approach to quantum stochastic processes
Von Waldenfels, Wilhelm
2014-01-01
This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. Considering in detail four basic examples (e.g. a two-level atom coupled to a heat bath of oscillators), in each case the Hamiltonian of the associated one-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors. Advanced topics include the theory of the Hudson-Parthasarathy equation and the amplified oscillator problem. To that end, a chapter on white noise calculus has also been included.
Modeling a SI epidemic with stochastic transmission: hyperbolic incidence rate.
Christen, Alejandra; Maulén-Yañez, M Angélica; González-Olivares, Eduardo; Curé, Michel
2018-03-01
In this paper a stochastic susceptible-infectious (SI) epidemic model is analysed, which is based on the model proposed by Roberts and Saha (Appl Math Lett 12: 37-41, 1999), considering a hyperbolic type nonlinear incidence rate. Assuming the proportion of infected population varies with time, our new model is described by an ordinary differential equation, which is analogous to the equation that describes the double Allee effect. The limit of the solution of this equation (deterministic model) is found when time tends to infinity. Then, the asymptotic behaviour of a stochastic fluctuation due to the environmental variation in the coefficient of disease transmission is studied. Thus a stochastic differential equation (SDE) is obtained and the existence of a unique solution is proved. Moreover, the SDE is analysed through the associated Fokker-Planck equation to obtain the invariant measure when the proportion of the infected population reaches steady state. An explicit expression for invariant measure is found and we study some of its properties. The long time behaviour of deterministic and stochastic models are compared by simulations. According to our knowledge this incidence rate has not been previously used for this type of epidemic models.
On the Radio-emitting Particles of the Crab Nebula: Stochastic Acceleration Model
Energy Technology Data Exchange (ETDEWEB)
Tanaka, Shuta J. [Department of Physics, Faculty of Science and Engineering, Konan University, 8-9-1 Okamoto, Kobe, Hyogo 658-8501 (Japan); Asano, Katsuaki, E-mail: sjtanaka@center.konan-u.ac.jp [Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa City, Chiba, 277-8582 (Japan)
2017-06-01
The broadband emission of pulsar wind nebulae (PWNe) is well described by non-thermal emissions from accelerated electrons and positrons. However, the standard shock acceleration model of PWNe does not account for the hard spectrum in radio wavelengths. The origin of the radio-emitting particles is also important to determine the pair production efficiency in the pulsar magnetosphere. Here, we propose a possible resolution for the particle energy distribution in PWNe; the radio-emitting particles are not accelerated at the pulsar wind termination shock but are stochastically accelerated by turbulence inside PWNe. We upgrade our past one-zone spectral evolution model to include the energy diffusion, i.e., the stochastic acceleration, and apply the model to the Crab Nebula. A fairly simple form of the energy diffusion coefficient is assumed for this demonstrative study. For a particle injection to the stochastic acceleration process, we consider the continuous injection from the supernova ejecta or the impulsive injection associated with supernova explosion. The observed broadband spectrum and the decay of the radio flux are reproduced by tuning the amount of the particle injected to the stochastic acceleration process. The acceleration timescale and the duration of the acceleration are required to be a few decades and a few hundred years, respectively. Our results imply that some unveiled mechanisms, such as back reaction to the turbulence, are required to make the energies of stochastically and shock-accelerated particles comparable.
Stochastic Modeling of Radioactive Material Releases
International Nuclear Information System (INIS)
Andrus, Jason; Pope, Chad
2015-01-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
Stochastic Modeling of Radioactive Material Releases
Energy Technology Data Exchange (ETDEWEB)
Andrus, Jason [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pope, Chad [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
A stochastic model for EEG microstate sequence analysis.
Gärtner, Matthias; Brodbeck, Verena; Laufs, Helmut; Schneider, Gaby
2015-01-01
The analysis of spontaneous resting state neuronal activity is assumed to give insight into the brain function. One noninvasive technique to study resting state activity is electroencephalography (EEG) with a subsequent microstate analysis. This technique reduces the recorded EEG signal to a sequence of prototypical topographical maps, which is hypothesized to capture important spatio-temporal properties of the signal. In a statistical EEG microstate analysis of healthy subjects in wakefulness and three stages of sleep, we observed a simple structure in the microstate transition matrix. It can be described with a first order Markov chain in which the transition probability from the current state (i.e., map) to a different map does not depend on the current map. The resulting transition matrix shows a high agreement with the observed transition matrix, requiring only about 2% of mass transport (1/2 L1-distance). In the second part, we introduce an extended framework in which the simple Markov chain is used to make inferences on a potential underlying time continuous process. This process cannot be directly observed and is therefore usually estimated from discrete sampling points of the EEG signal given by the local maxima of the global field power. Therefore, we propose a simple stochastic model called sampled marked intervals (SMI) model that relates the observed sequence of microstates to an assumed underlying process of background intervals and thus, complements approaches that focus on the analysis of observable microstate sequences. Copyright © 2014 Elsevier Inc. All rights reserved.
Stochastic Dynamics on Hypergraphs and the Spatial Majority Rule Model
Lanchier, N.; Neufer, J.
2013-04-01
This article starts by introducing a new theoretical framework to model spatial systems which is obtained from the framework of interacting particle systems by replacing the traditional graphical structure that defines the network of interactions with a structure of hypergraph. This new perspective is more appropriate to define stochastic spatial processes in which large blocks of vertices may flip simultaneously, which is then applied to define a spatial version of the Galam's majority rule model. In our spatial model, each vertex of the lattice has one of two possible competing opinions, say opinion 0 and opinion 1, as in the popular voter model. Hyperedges are updated at rate one, which results in all the vertices in the hyperedge changing simultaneously their opinion to the majority opinion of the hyperedge. In the case of a tie in hyperedges with even size, a bias is introduced in favor of type 1, which is motivated by the principle of social inertia. Our analytical results along with simulations and heuristic arguments suggest that, in any spatial dimensions and when the set of hyperedges consists of the collection of all n×⋯× n blocks of the lattice, opinion 1 wins when n is even while the system clusters when n is odd, which contrasts with results about the voter model in high dimensions for which opinions coexist. This is fully proved in one dimension while the rest of our analysis focuses on the cases when n=2 and n=3 in two dimensions.
Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.
Directory of Open Access Journals (Sweden)
Hendrik Baumann
Full Text Available Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.
Numerical Integration of the Master Equation in Some Models of Stochastic Epidemiology
Jenkinson, Garrett; Goutsias, John
2012-01-01
The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation – up to a desired precision – in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1. PMID:22615755
Bayesian parameter estimation for stochastic models of biological cell migration
Dieterich, Peter; Preuss, Roland
2013-08-01
Cell migration plays an essential role under many physiological and patho-physiological conditions. It is of major importance during embryonic development and wound healing. In contrast, it also generates negative effects during inflammation processes, the transmigration of tumors or the formation of metastases. Thus, a reliable quantification and characterization of cell paths could give insight into the dynamics of these processes. Typically stochastic models are applied where parameters are extracted by fitting models to the so-called mean square displacement of the observed cell group. We show that this approach has several disadvantages and problems. Therefore, we propose a simple procedure directly relying on the positions of the cell's trajectory and the covariance matrix of the positions. It is shown that the covariance is identical with the spatial aging correlation function for the supposed linear Gaussian models of Brownian motion with drift and fractional Brownian motion. The technique is applied and illustrated with simulated data showing a reliable parameter estimation from single cell paths.
A continuous stochastic model for non-equilibrium dense gases
Sadr, M.; Gorji, M. H.
2017-12-01
While accurate simulations of dense gas flows far from the equilibrium can be achieved by direct simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order to cope with that, an efficient yet accurate solution algorithm based on the Fokker-Planck approximation of the Enskog equation is devised in this paper; the approximation is very much associated with the Fokker-Planck model derived from the Boltzmann equation by Jenny et al. ["A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion," J. Comput. Phys. 229, 1077-1098 (2010)] and Gorji et al. ["Fokker-Planck model for computational studies of monatomic rarefied gas flows," J. Fluid Mech. 680, 574-601 (2011)]. The idea behind these Fokker-Planck descriptions is to project the dynamics of discrete collisions implied by the molecular encounters into a set of continuous Markovian processes subject to the drift and diffusion. Thereby, the evolution of particles representing the governing stochastic process becomes independent from each other and thus very efficient numerical schemes can be constructed. By close inspection of the Enskog operator, it is observed that the dense gas effects contribute further to the advection of molecular quantities. That motivates a modelling approach where the dense gas corrections can be cast in the extra advection of particles. Therefore, the corresponding Fokker-Planck approximation is derived such that the evolution in the physical space accounts for the dense effects present in the pressure, stress tensor, and heat fluxes. Hence the consistency between the devised Fokker-Planck approximation and the Enskog operator is shown for the velocity moments up to the heat fluxes. For validation studies, a homogeneous gas inside a box besides Fourier, Couette, and lid-driven cavity flow setups is considered. The results based on the Fokker-Planck model are
A stochastic discrete optimization model for designing container terminal facilities
Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista
2017-11-01
As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.
Stochastic many-particle model for LFP electrodes
Guhlke, Clemens; Gajewski, Paul; Maurelli, Mario; Friz, Peter K.; Dreyer, Wolfgang
2018-02-01
In the framework of non-equilibrium thermodynamics, we derive a new model for many-particle electrodes. The model is applied to LiFePO4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by both different particle sizes and surface fluctuations leading to a system of stochastic differential equations. An explicit relation between battery voltage and current controlled by the thermodynamic state variables is derived. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate-limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate-limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltage-charge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.
Stochastic Modelling and Optimization of Complex Infrastructure Systems
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In this paper it is shown that recent progress in stochastic modelling and optimization in combination with advanced computer systems has now made it possible to improve the design and the maintenance strategies for infrastructure systems. The paper concentrates on highway networks and single large...
Optimal Tax Reduction by Depreciation : A Stochastic Model
Berg, M.; De Waegenaere, A.M.B.; Wielhouwer, J.L.
1996-01-01
This paper focuses on the choice of a depreciation method, when trying to minimize the expected value of the present value of future tax payments.In a quite general model that allows for stochastic future cash- ows and a tax structure with tax brackets, we determine the optimal choice between the
A stochastic model for forecast consumption in master scheduling
Weeda, P.J.; Weeda, P.J.
1994-01-01
This paper describes a stochastic model for the reduction of the initial forecast in the Master Schedule (MS) of an MRP system during progress of time by the acceptance of customer orders. Results are given for the expectation and variance of the number of yet unknown deliveries as a function of
Stochastic model of thin market with an indivisible commodity
Czech Academy of Sciences Publication Activity Database
Šmíd, Martin
2005-01-01
Roč. 13, č. 1 (2005), s. 94-100 ISSN 0572-3043 R&D Projects: GA ČR GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : thin market * market price * stochastic models Subject RIV: AH - Economics
Time Ordering in Frontal Lobe Patients: A Stochastic Model Approach
Magherini, Anna; Saetti, Maria Cristina; Berta, Emilia; Botti, Claudio; Faglioni, Pietro
2005-01-01
Frontal lobe patients reproduced a sequence of capital letters or abstract shapes. Immediate and delayed reproduction trials allowed the analysis of short- and long-term memory for time order by means of suitable Markov chain stochastic models. Patients were as proficient as healthy subjects on the immediate reproduction trial, thus showing spared…
Integrated Human Behavior Modeling and Stochastic Control (IHBMSC)
2014-08-01
angle, dwell time, workload). For a 50% target density scenario where the operator discrimination task is fairly difficult, the integrated human ... behavior model and stochastic controller (IHBMSC) was shown to reduce the FA rate from 35% to 5%. Also, the IHBMSC performance was found to be quite robust for lower target densities (5%) and different operators.
Probability density estimation in stochastic environmental models using reverse representations
Van den Berg, E.; Heemink, A.W.; Lin, H.X.; Schoenmakers, J.G.M.
2003-01-01
The estimation of probability densities of variables described by systems of stochastic dierential equations has long been done using forward time estimators, which rely on the generation of realizations of the model, forward in time. Recently, an estimator based on the combination of forward and
A simple stochastic weather generator for ecological modeling
A.G. Birt; M.R. Valdez-Vivas; R.M. Feldman; C.W. Lafon; D. Cairns; R.N. Coulson; M. Tchakerian; W. Xi; Jim Guldin
2010-01-01
Stochastic weather generators are useful tools for exploring the relationship between organisms and their environment. This paper describes a simple weather generator that can be used in ecological modeling projects. We provide a detailed description of methodology, and links to full C++ source code (http://weathergen.sourceforge.net) required to implement or modify...
Stochastic disturbance rejection in model predictive control by randomized algorithms
Batina, Ivo; Stoorvogel, Antonie Arij; Weiland, Siep
2001-01-01
In this paper we consider model predictive control with stochastic disturbances and input constraints. We present an algorithm which can solve this problem approximately but with arbitrary high accuracy. The optimization at each time step is a closed loop optimization and therefore takes into
Hydrological modeling using a multi-site stochastic weather generator
Weather data is usually required at several locations over a large watershed, especially when using distributed models for hydrological simulations. In many applications, spatially correlated weather data can be provided by a multi-site stochastic weather generator which considers the spatial correl...
Application of a stochastic modelling framework to characterize the ...
Indian Academy of Sciences (India)
Home; Journals; Sadhana; Volume 36; Issue 4. Application of a stochastic modelling framework to characterize the inﬂuence of different oxide scales on the solid particle erosion behaviour of boiler grade steel. S K Das. Volume 36 Issue 4 August 2011 pp 425-440 ...
Latent Stochastic Actor Oriented Models for Relational Event Data
2012-03-15
L-SAOMs for Relational Events Latent Stochastic Actor Oriented Models for Relational Event Data J.A. Lospinoso12 J.H. Koskinen2 T.A.B. Snijders2......PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US
A stochastic large deformation model for computational anatomy
DEFF Research Database (Denmark)
Arnaudon, Alexis; Holm, Darryl D.; Pai, Akshay Sadananda Uppinakudru
2017-01-01
In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation...
Stochastic finite-fault modelling of strong earthquakes in Narmada ...
Indian Academy of Sciences (India)
Stochastic finite fault modelling of strong earthquakes. 839. 1983). It has been widely used to predict the ground motion around the globe where earthquake recordings are scanty. The conventional point source approximation is unable to characterize key features of ground motions from large earthquakes, such as their ...
Experimental Investigation and Stochastic Modelling of the Fatigue Behaviour of Welded Steel Joints
DEFF Research Database (Denmark)
Lassen, Tom
The present report describes the fatigue behaviour of surface cracks in welded steel joints. Emphasis is laid on fracture mechanics modelling and the stochastic nature of the fatigue process. Various sources which may contribute to the observed scatter in time to crack initiation and time spent...
Stochastic evolution of the Universe: A possible dynamical process ...
Indian Academy of Sciences (India)
C Sivakumar
2017-12-11
Dec 11, 2017 ... Abstract. In this paper, we propose a stochastic evolution of the early Universe which can lead to a fractal correlation in galactic distribution in the Universe. The stochastic equation of state, due to fluctuating creation rates of various components in a many-component fluid, leads to a fluctuating expansion ...
Stochastic evolution of the Universe: A possible dynamical process ...
Indian Academy of Sciences (India)
In this paper, we propose a stochastic evolution of the early Universe which can lead to a fractal correlation in galactic distribution in the Universe. The stochastic equation of state, due to fluctuating creation rates of various components in a many-component fluid, leads to a fluctuating expansion rate for the Universe in the ...
A Stochastic Approach to Noise Modeling for Barometric Altimeters
Directory of Open Access Journals (Sweden)
Angelo Maria Sabatini
2013-11-01
Full Text Available The question whether barometric altimeters can be applied to accurately track human motions is still debated, since their measurement performance are rather poor due to either coarse resolution or drifting behavior problems. As a step toward accurate short-time tracking of changes in height (up to few minutes, we develop a stochastic model that attempts to capture some statistical properties of the barometric altimeter noise. The barometric altimeter noise is decomposed in three components with different physical origin and properties: a deterministic time-varying mean, mainly correlated with global environment changes, and a first-order Gauss-Markov (GM random process, mainly accounting for short-term, local environment changes, the effects of which are prominent, respectively, for long-time and short-time motion tracking; an uncorrelated random process, mainly due to wideband electronic noise, including quantization noise. Autoregressive-moving average (ARMA system identification techniques are used to capture the correlation structure of the piecewise stationary GM component, and to estimate its standard deviation, together with the standard deviation of the uncorrelated component. M-point moving average filters used alone or in combination with whitening filters learnt from ARMA model parameters are further tested in few dynamic motion experiments and discussed for their capability of short-time tracking small-amplitude, low-frequency motions.
Parameter estimation in stochastic rainfall-runoff models
DEFF Research Database (Denmark)
Jonsdottir, Harpa; Madsen, Henrik; Palsson, Olafur Petur
2006-01-01
A parameter estimation method for stochastic rainfall-runoff models is presented. The model considered in the paper is a conceptual stochastic model, formulated in continuous-discrete state space form. The model is small and a fully automatic optimization is, therefore, possible for estimating all....... For a comparison the parameters are also estimated by an output error method, where the sum of squared simulation error is minimized. The former methodology is optimal for short-term prediction whereas the latter is optimal for simulations. Hence, depending on the purpose it is possible to select whether...... the parameter values are optimal for simulation or prediction. The data originates from Iceland and the model is designed for Icelandic conditions, including a snow routine for mountainous areas. The model demands only two input data series, precipitation and temperature and one output data series...
Economic-Oriented Stochastic Optimization in Advanced Process Control of Chemical Processes
Dobos, László; Király, András; Abonyi, János
2012-01-01
Finding the optimal operating region of chemical processes is an inevitable step toward improving economic performance. Usually the optimal operating region is situated close to process constraints related to product quality or process safety requirements. Higher profit can be realized only by assuring a relatively low frequency of violation of these constraints. A multilevel stochastic optimization framework is proposed to determine the optimal setpoint values of control loops with respect t...
Stochastic model of Zipf's law and the universality of the power-law exponent.
Yamamoto, Ken
2014-04-01
We propose a stochastic model of Zipf's law, namely a power-law relation between rank and size, and clarify as to why a specific value of its power-law exponent is quite universal. We focus on the successive total of a multiplicative stochastic process. By employing properties of a well-known stochastic process, we concisely show that the successive total follows a stationary power-law distribution, which is directly related to Zipf's law. The formula of the power-law exponent is also derived. Finally, we conclude that the universality of the rank-size exponent is brought about by symmetry between an increase and a decrease in the random growth rate.
Stochastic Mixing Model with Power Law Decay of Variance
Fedotov, S.; Ihme, M.; Pitsch, H.
2003-01-01
Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.
Epigenetics and Evolution: Transposons and the Stochastic Epigenetic Modification Model
Sergio Branciamore; Andrei S. Rodin; Grigoriy Gogoshin; Arthur D. Riggs
2015-01-01
In addition to genetic variation, epigenetic variation and transposons can greatly affect the evolutionary fitnesses landscape and gene expression. Previously we proposed a mathematical treatment of a general epigenetic variation model that we called Stochastic Epigenetic Modification (SEM) model. In this study we follow up with a special case, the Transposon Silencing Model (TSM), with, once again, emphasis on quantitative treatment. We have investigated the evolutionary effects of epigeneti...
Stochastic model for gene transcription on Drosophila melanogaster embryos
Prata, Guilherme N.; Hornos, José Eduardo M.; Ramos, Alexandre F.
2016-02-01
We examine immunostaining experimental data for the formation of stripe 2 of even-skipped (eve) transcripts on D. melanogaster embryos. An estimate of the factor converting immunofluorescence intensity units into molecular numbers is given. The analysis of the eve dynamics at the region of stripe 2 suggests that the promoter site of the gene has two distinct regimes: an earlier phase when it is predominantly activated until a critical time when it becomes mainly repressed. That suggests proposing a stochastic binary model for gene transcription on D. melanogaster embryos. Our model has two random variables: the transcripts number and the state of the source of mRNAs given as active or repressed. We are able to reproduce available experimental data for the average number of transcripts. An analysis of the random fluctuations on the number of eves and their consequences on the spatial precision of stripe 2 is presented. We show that the position of the anterior or posterior borders fluctuate around their average position by ˜1 % of the embryo length, which is similar to what is found experimentally. The fitting of data by such a simple model suggests that it can be useful to understand the functions of randomness during developmental processes.