Stationary stochastic processes theory and applications

CERN Document Server

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 of volatility in continuous time

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole; Veraart, Almut

This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility...... of volatility can be defined both non-parametrically, where we link it to the quadratic variation of the stochastic variance process, and parametrically, where we propose two new SV models which allow for stochastic volatility of volatility. In addition, we show that volatility of volatility can be estimated...

Composite stochastic processes

NARCIS (Netherlands)

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

Strategic WIP Inventory Positioning for Make-to-Order Production with Stochastic Processing Times

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Jingjing Jiang

2017-01-01

Full Text Available It is vital for make-to-order manufacturers to shorten the lead time to meet the customers’ requirements. Holding work-in-process (WIP inventory at more stations can reduce the lead time, but it also brings about higher inventory holding cost. Therefore, it is important to seek out the optimal set of stations to hold WIP inventory to minimize the total inventory holding cost, while meeting the required due date for the final product at the same time. Since the problem with deterministic processing times at the stations has been addressed, as a natural extension, in this study, we address the problem with stochastic processing times, which is more realistic in the manufacturing environment. Assuming that the processing times follow normal distributions, we propose a solution procedure using genetic algorithm.

Stochastic time series analysis of hydrology data for water resources

Science.gov (United States)

Sathish, S.; Khadar Babu, S. K.

2017-11-01

The prediction to current publication of stochastic time series analysis in hydrology and seasonal stage. The different statistical tests for predicting the hydrology time series on Thomas-Fiering model. The hydrology time series of flood flow have accept a great deal of consideration worldwide. The concentration of stochastic process areas of time series analysis method are expanding with develop concerns about seasonal periods and global warming. The recent trend by the researchers for testing seasonal periods in the hydrologic flowseries using stochastic process on Thomas-Fiering model. The present article proposed to predict the seasonal periods in hydrology using Thomas-Fiering model.

Essentials of stochastic processes

CERN Document Server

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...

Factors influencing lysis time stochasticity in bacteriophage λ

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Dennehy John J

2011-08-01

Full Text Available Abstract Background Despite identical genotypes and seemingly uniform environments, stochastic gene expression and other dynamic intracellular processes can produce considerable phenotypic diversity within clonal microbes. One trait that provides a good model to explore the molecular basis of stochastic variation is the timing of host lysis by bacteriophage (phage. Results Individual lysis events of thermally-inducible λ lysogens were observed using a temperature-controlled perfusion chamber mounted on an inverted microscope. Both mean lysis time (MLT and its associated standard deviation (SD were estimated. Using the SD as a measure of lysis time stochasticity, we showed that lysogenic cells in controlled environments varied widely in lysis times, and that the level of lysis time stochasticity depended on allelic variation in the holin sequence, late promoter (pR' activity, and host growth rate. In general, the MLT was positively correlated with the SD. Both lower pR' activities and lower host growth rates resulted in larger SDs. Results from premature lysis, induced by adding KCN at different time points after lysogen induction, showed a negative correlation between the timing of KCN addition and lysis time stochasticity. Conclusions Taken together with results published by others, we conclude that a large fraction of λ lysis time stochasticity is the result of random events following the expression and diffusion of the holin protein. Consequently, factors influencing the timing of reaching critical holin concentrations in the cell membrane, such as holin production rate, strongly influence the mean lysis time and the lysis time stochasticity.

Stochastic ℋ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss

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Yingqi Zhang

2012-01-01

Full Text Available This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.

Stochastic processes inference theory

CERN Document Server

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.

Time-ordered product expansions for computational stochastic system biology

International Nuclear Information System (INIS)

Mjolsness, Eric

2013-01-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie’s stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems. (paper)

Stochastic processes and applications diffusion processes, the Fokker-Planck and Langevin equations

CERN Document Server

Pavliotis, Grigorios A

2014-01-01

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated.                 The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to eq...

Forecasting financial asset processes: stochastic dynamics via learning neural networks.

Science.gov (United States)

Giebel, S; Rainer, M

2010-01-01

Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.

Anomalous scaling of stochastic processes and the Moses effect.

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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.

Anomalous scaling of stochastic processes and the Moses effect

Science.gov (United States)

Chen, Lijian; Bassler, Kevin E.; McCauley, Joseph L.; Gunaratne, Gemunu H.

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t1/2. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Modelling and application of stochastic processes

CERN Document Server

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,...

Superior memory efficiency of quantum devices for the simulation of continuous-time stochastic processes

Science.gov (United States)

Elliott, Thomas J.; Gu, Mile

2018-03-01

Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine.

An introduction to probability and stochastic processes

CERN Document Server

Melsa, James L

2013-01-01

Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.

Stochastic calculus for uncoupled continuous-time random walks.

Science.gov (United States)

Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L

2009-06-01

The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy alpha -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.

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)

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Science.gov (United States)

Williams Colin P.

1999-01-01

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Investment timing under hybrid stochastic and local volatility

International Nuclear Information System (INIS)

Kim, Jeong-Hoon; Lee, Min-Ku; Sohn, So Young

2014-01-01

Highlights: • The effects of hybrid stochastic volatility on real option prices are studied. • The stochastic volatility consists of a fast mean-reverting component and a CEV type one. • A fast mean-reverting factor lowers real option prices and investment thresholds. • The increase of elasticity raises real option prices and investment thresholds. • The effects of the addition of a slowly varying factor depend upon the project value. - Abstract: We consider an investment timing problem under a real option model where the instantaneous volatility of the project value is given by a combination of a hidden stochastic process and the project value itself. The stochastic volatility part is given by a function of a fast mean-reverting process as well as a slowly varying process and the local volatility part is a power (the elasticity parameter) of the project value itself. The elasticity parameter controls directly the correlation between the project value and the volatility. Knowing that the project value represents the market price of a real asset in many applications and the value of the elasticity parameter depends on the asset, the elasticity parameter should be treated with caution for investment decision problems. Based on the hybrid structure of volatility, we investigate the simultaneous impact of the elasticity and the stochastic volatility on the real option value as well as the investment threshold

Low Variance Couplings for Stochastic Models of Intracellular Processes with Time-Dependent Rate Functions.

Science.gov (United States)

Anderson, David F; Yuan, Chaojie

2018-04-18

A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an exceptionally low variance between the generated paths. This coupling will be useful in the numerical computation of parametric sensitivities and the fast estimation of expectations via multilevel Monte Carlo methods. We provide the requisite estimators in both cases.

On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout

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Yingqi Zhang

2012-01-01

Full Text Available This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.

Simulation of anaerobic digestion processes using stochastic algorithm.

Science.gov (United States)

Palanichamy, Jegathambal; Palani, Sundarambal

2014-01-01

The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic digestion systems. Although several models have been developed, mostly they suffer from lack of knowledge on constants, complexity and weak generalization. The basis of the deterministic approach for modelling the physico and bio-chemical reactions occurring in the AD system is the law of mass action, which gives the simple relationship between the reaction rates and the species concentrations. The assumptions made in the deterministic models are not hold true for the reactions involving chemical species of low concentration. The stochastic behaviour of the physicochemical processes can be modeled at mesoscopic level by application of the stochastic algorithms. In this paper a stochastic algorithm (Gillespie Tau Leap Method) developed in MATLAB was applied to predict the concentration of glucose, acids and methane formation at different time intervals. By this the performance of the digester system can be controlled. The processes given by ADM1 (Anaerobic Digestion Model 1) were taken for verification of the model. The proposed model was verified by comparing the results of Gillespie's algorithms with the deterministic solution for conversion of glucose into methane through degraders. At higher value of 'τ' (timestep), the computational time required for reaching the steady state is more since the number of chosen reactions is less. When the simulation time step is reduced, the results are similar to ODE solver. It was concluded that the stochastic algorithm is a suitable approach for the simulation of complex anaerobic digestion processes. The accuracy of the results depends on the optimum selection of tau value.

Stochastic stability of mechanical systems under renewal jump process parametric excitation

DEFF Research Database (Denmark)

Iwankiewicz, R.; Nielsen, Søren R.K.; Larsen, Jesper Winther

2005-01-01

independent, negative exponential distributed variables; hence, the arrival process may be termed as a generalized Erlang renewal process. The excitation process is governed by the stochastic equation driven by two independent Poisson processes, with different parameters. If the response in a single mode...... is investigated, the problem is governed in the state space by two stochastic equations, because the stochastic equation for the excitation process is autonomic. However due to the parametric nature of the excitation, the nonlinear term appears at the right-hand sides of the equations. The equations become linear...... of the stochastic equation governing the natural logarithm of the hyperspherical amplitude process and using the modification of the method wherein the time averaging of the pertinent expressions is replaced by ensemble averaging. It is found that the direct simulation is more suitable and that the asymptotic mean...

Mathematical statistics and stochastic processes

CERN Document Server

Bosq, Denis

2013-01-01

Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob

Simulation and inference for stochastic processes with YUIMA a comprehensive R framework for SDEs and other stochastic processes

CERN Document Server

Iacus, Stefano M

2018-01-01

The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these ...

Quantization by stochastic relaxation processes and supersymmetry

International Nuclear Information System (INIS)

Kirschner, R.

1984-01-01

We show the supersymmetry mechanism resposible for the quantization by stochastic relaxation processes and for the effective cancellation of the additional time dimension against the two Grassmann dimensions. We give a non-perturbative proof of the validity of this quantization procedure. (author)

Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process

Science.gov (United States)

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.

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

Stochastic Simulation of Process Calculi for Biology

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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.

Neural network connectivity and response latency modelled by stochastic processes

DEFF Research Database (Denmark)

Tamborrino, Massimiliano

is connected to thousands of other neurons. The rst question is: how to model neural networks through stochastic processes? A multivariate Ornstein-Uhlenbeck process, obtained as a diffusion approximation of a jump process, is the proposed answer. Obviously, dependencies between neurons imply dependencies......Stochastic processes and their rst passage times have been widely used to describe the membrane potential dynamics of single neurons and to reproduce neuronal spikes, respectively.However, cerebral cortex in human brains is estimated to contain 10-20 billions of neurons and each of them...... between their spike times. Therefore, the second question is: how to detect neural network connectivity from simultaneously recorded spike trains? Answering this question corresponds to investigate the joint distribution of sequences of rst passage times. A non-parametric method based on copulas...

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 betwe...... 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....

Ranking shortest paths in Stochastic time-denpendent networks

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...

K shortest paths in stochastic time-dependent networks

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Pretolani, Daniele; Andersen, Kim Allan

2004-01-01

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...

Verification of Stochastic Process Calculi

DEFF Research Database (Denmark)

Skrypnyuk, Nataliya

algorithms for constructing bisimulation relations, computing (overapproximations of) sets of reachable states and computing the expected time reachability, the last for a linear fragment of IMC. In all the cases we have the complexities of algorithms which are low polynomial in the size of the syntactic....... 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...... of Interactive Markov Chains (IMC). We have devised the Pathway Analysis of IMC that is not only correct in the sense of overapproximating all possible behaviour scenarios, as is usual for Static Analysis methods, but is also precise. This gives us the possibility to explicitly decide on the trade-o between...

A Time-Variant Reliability Model for Copper Bending Pipe under Seawater-Active Corrosion Based on the Stochastic Degradation Process

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.

Stochastic lag time in nucleated linear self-assembly

Energy Technology Data Exchange (ETDEWEB)

Tiwari, Nitin S. [Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Schoot, Paul van der [Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)

2016-06-21

Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerization reactions. One of the most important characteristic features in this kind of problem is the existence of a lag phase before self-assembly takes off, which is what we focus attention on. We study the associated lag time as a function of system size and kinetic pathway. We find that the leading order stochastic contribution to the lag time before polymerization commences is inversely proportional to the system volume for large-enough system size for all nine reaction pathways tested. Finite-size corrections to this do depend on the kinetic pathway.

Quantum mechanics and stochastic mechanics for compatible observables at different times

International Nuclear Information System (INIS)

Correggi, M.; Morchio, G.

2002-01-01

Bohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the presence of noninteracting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary states agree with quantum mechanics only in the case of product wave functions. By appropriate Bell-like inequalities it is shown that no classical theory, in particular no stochastic process, can reproduce the quantum mechanical correlations of position variables of noninteracting systems at different times

Probability, Statistics, and Stochastic Processes

CERN Document Server

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

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...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...

Convergence of trajectories in fractal interpolation of stochastic processes

International Nuclear Information System (INIS)

MaIysz, Robert

2006-01-01

The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation

Levy-Student processes for a stochastic model of beam halos

Energy Technology Data Exchange (ETDEWEB)

Petroni, N. Cufaro [Department of Mathematics, University of Bari, and INFN Sezione di Bari, via E. Orabona 4, 70125 Bari (Italy)]. E-mail: cufaro@ba.infn.it; De Martino, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); De Siena, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); Illuminati, F. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy)

2006-06-01

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will analyze this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) stochastic model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. In the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.

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

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...

Empirical method to measure stochasticity and multifractality in nonlinear time series

Science.gov (United States)

Lin, Chih-Hao; Chang, Chia-Seng; Li, Sai-Ping

2013-12-01

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.

Modelling and simulating decision processes of linked lives: An approach based on concurrent processes and stochastic race.

Science.gov (United States)

Warnke, Tom; Reinhardt, Oliver; Klabunde, Anna; Willekens, Frans; Uhrmacher, Adelinde M

2017-10-01

Individuals' decision processes play a central role in understanding modern migration phenomena and other demographic processes. Their integration into agent-based computational demography depends largely on suitable support by a modelling language. We are developing the Modelling Language for Linked Lives (ML3) to describe the diverse decision processes of linked lives succinctly in continuous time. The context of individuals is modelled by networks the individual is part of, such as family ties and other social networks. Central concepts, such as behaviour conditional on agent attributes, age-dependent behaviour, and stochastic waiting times, are tightly integrated in the language. Thereby, alternative decisions are modelled by concurrent processes that compete by stochastic race. Using a migration model, we demonstrate how this allows for compact description of complex decisions, here based on the Theory of Planned Behaviour. We describe the challenges for the simulation algorithm posed by stochastic race between multiple concurrent complex decisions.

Introduction to probability and stochastic processes with applications

CERN Document Server

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

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

Fourier analysis and stochastic processes

CERN Document Server

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...

Lectures on Topics in Spatial Stochastic Processes

CERN Document Server

Capasso, Vincenzo; Ivanoff, B Gail; Dozzi, Marco; Dalang, Robert C; Mountford, Thomas S

2003-01-01

The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.

Stochastic transport processes in discrete biological systems

CERN Document Server

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...

Bidirectional Classical Stochastic Processes with Measurements and Feedback

Science.gov (United States)

Hahne, G. E.

2005-01-01

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Discrete stochastic processes and applications

CERN Document Server

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.

Approximation of itô integrals arising in stochastic time-delayed systems

NARCIS (Netherlands)

Bagchi, Arunabha

1984-01-01

Likelihood functional for stochastic linear time-delayed systems involve Itô integrals with respect to the observed data. Since the Wiener process appearing in the standard observation process model for such systems is not realizable and the physically observed process is smooth, one needs to study

Stochastic Processes in Finance and Behavioral Finance

OpenAIRE

Steinbacher, Matjaz

2008-01-01

In the paper, we put some foundations for studying asset pricing and finance as a stochastic and behavioral process. In such process, preferences and psychology of agents represent the most important factor in the decision-making of people. Individuals have their own ways of acquiring the information they need, how to deal with them and how to make predictions and decisions. People usually also do not behave consistent in time, but learn. Therefore, in order to understand the behavior on the ...

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....

Importance Sampling for Stochastic Timed Automata

DEFF Research Database (Denmark)

Jegourel, Cyrille; Larsen, Kim Guldstrand; Legay, Axel

2016-01-01

We present an importance sampling framework that combines symbolic analysis and simulation to estimate the probability of rare reachability properties in stochastic timed automata. By means of symbolic exploration, our framework first identifies states that cannot reach the goal. A state-wise cha......We present an importance sampling framework that combines symbolic analysis and simulation to estimate the probability of rare reachability properties in stochastic timed automata. By means of symbolic exploration, our framework first identifies states that cannot reach the goal. A state...

Explicit calibration and simulation of stochastic fields by low-order ARMA processes

DEFF Research Database (Denmark)

Krenk, Steen

2011-01-01

A simple framework for autoregressive simulation of stochastic fields is presented. The autoregressive format leads to a simple exponential correlation structure in the time-dimension. In the case of scalar processes a more detailed correlation structure can be obtained by adding memory...... to the process via an extension to autoregressive moving average (ARMA) processes. The ARMA format incorporates a more detailed correlation structure by including previous values of the simulated process. Alternatively, a more detailed correlation structure can be obtained by including additional 'state......-space' variables in the simulation. For a scalar process this would imply an increase of the dimension of the process to be simulated. In the case of a stochastic field the correlation in the time-dimension is represented, although indirectly, in the simultaneous spatial correlation. The model with the shortest...

Absolute continuity under time shift of trajectories and related stochastic calculus

CERN Document Server

Löbus, Jörg-Uwe

2017-01-01

The text is concerned with a class of two-sided stochastic processes of the form X=W+A. Here W is a two-sided Brownian motion with random initial data at time zero and A\\equiv A(W) is a function of W. Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when A is a jump process. Absolute continuity of (X,P) under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, m, and on A with A_0=0 we verify \\frac{P(dX_{\\cdot -t})}{P(dX_\\cdot)}=\\frac{m(X_{-t})}{m(X_0)}\\cdot \\prod_i\\left|\

Bridging time scales in cellular decision making with a stochastic bistable switch

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Waldherr Steffen

2010-08-01

Full Text Available Abstract Background Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. Some of these transformations act over a very long time scale on the cell population level, up to the entire lifespan of the organism. Results In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Conclusions Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.

Analyzing a stochastic time series obeying a second-order differential equation.

Science.gov (United States)

Lehle, B; Peinke, J

2015-06-01

The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.

Stochastic processes dominate during boreal bryophyte community assembly.

Science.gov (United States)

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

Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes

International Nuclear Information System (INIS)

Arenas, Zochil González; Barci, Daniel G

2012-01-01

Multiplicative white-noise stochastic processes continue to attract attention in a wide area of scientific research. The variety of prescriptions available for defining them makes the development of general tools for their characterization difficult. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for such processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassmann formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of the equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints that it imposes on correlation functions using Ward–Takahashi identities. (paper)

Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes

Science.gov (United States)

González Arenas, Zochil; Barci, Daniel G.

2012-12-01

Multiplicative white-noise stochastic processes continue to attract attention in a wide area of scientific research. The variety of prescriptions available for defining them makes the development of general tools for their characterization difficult. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for such processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassmann formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of the equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints that it imposes on correlation functions using Ward-Takahashi identities.

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 differential equation model for linear growth birth and death processes with immigration and emigration

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

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

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.

Long-time correlations in the stochastic regime

International Nuclear Information System (INIS)

Karney, C.F.F.

1982-11-01

The phase space for Hamiltonians of two degrees of freedom is usually divided into stochastic and integrable components. Even when well into the stochastic regime, integrable orbits may surround small stable regions or islands. The effect of these islands on the correlation function for the stochastic trajectories is examined. Depending on the value of the parameter describing the rotation number for the elliptic fixed point at the center of the island, the long-time correlation function may decay as t -5 or exponentially, but more commonly it decays much more slowly (roughly as t -1 ). As a consequence these small islands may have a profound effect on the properties such as the diffusion coefficient, of the stochastic orbits

Research in Stochastic Processes.

Science.gov (United States)

1982-10-31

Office of Scientific Research Grant AFOSR F49620 82 C 0009 Period: 1 Noveber 1981 through 31 October 1982 Title: Research in Stochastic Processes Co...STA4ATIS CAMBANIS The work briefly described here was developed in connection with problems arising from and related to the statistical comunication

A compositional Translation of Stochastic Automata into Timed Automata

NARCIS (Netherlands)

d' Argenio, P.R.

We present a translation from stochastic automata [17, 16] into timed automata with deadlines [37, 13]. The translation preserves traces when the stochastic characteristics, namely the probability measures, are abstracted from the original stochastic automaton. Moreover, we show that the translation

Structure and Randomness of Continuous-Time, Discrete-Event Processes

Science.gov (United States)

Marzen, Sarah E.; Crutchfield, James P.

2017-10-01

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (ɛ -machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.

Doubly stochastic Poisson processes in artificial neural learning.

Science.gov (United States)

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Stochastic Approach to Determine CO2 Hydrate Induction Time in Clay Mineral Suspensions

Science.gov (United States)

Lee, K.; Lee, S.; Lee, W.

2008-12-01

A large number of induction time data for carbon dioxide hydrate formation were obtained from a batch reactor consisting of four independent reaction cells. Using resistance temperature detector(RTD)s and a digital microscope, we successfully monitored the whole process of hydrate formation (i.e., nucleation and crystal growth) and detected the induction time. The experiments were carried out in kaolinite and montmorillonite suspensions at temperatures between 274 and 277 K and pressures ranging from 3.0 to 4.0 MPa. Each set of data was analyzed beforehand whether to be treated by stochastic manner or not. Geochemical factors potentially influencing the hydrate induction time under different experimental conditions were investigated by stochastic analyses. We observed that clay mineral type, pressure, and temperature significantly affect the stochastic behavior of the induction times for CO2 hydrate formation in this study. The hydrate formation kinetics along with stochastic analyses can provide basic understanding for CO2 hydrate storage in deep-sea sediment and geologic formation, securing its stability under the environments.

Stochastic space-time and quantum theory

International Nuclear Information System (INIS)

Frederick, C.

1976-01-01

Much of quantum mechanics may be derived if one adopts a very strong form of Mach's principle such that in the absence of mass, space-time becomes not flat, but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic-metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can obtain an explanation of conjugate variables and also a derivation of the uncertainty principle. Finally the superposition of stochastic metrics and the identification of root -g in the four-dimensional invariant volume element root -g dV as the indicator of relative probability yields the phenomenon of interference as will be described for the two-slit experiment

Learning Theory Estimates with Observations from General Stationary Stochastic Processes.

Science.gov (United States)

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.

Stochastic resonance during a polymer translocation process

International Nuclear Information System (INIS)

Mondal, Debasish; Muthukumar, M.

2016-01-01

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

An adaptive algorithm for simulation of stochastic reaction-diffusion processes

International Nuclear Information System (INIS)

Ferm, Lars; Hellander, Andreas; Loetstedt, Per

2010-01-01

We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.

Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

Energy Technology Data Exchange (ETDEWEB)

Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com [Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce (Turkey); Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr [Department of Mathematics, Institute of Science and Arts, Afyon Kocatepe University, Afyonkarahisar (Turkey); Çelik, Nuri, E-mail: ncelik@bartin.edu.tr [Department of Statistics, Faculty of Science, Bartın University, Bartın-Turkey (Turkey)

2016-04-18

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

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

Evolution and mass extinctions as lognormal stochastic processes

Science.gov (United States)

Maccone, Claudio

2014-10-01

In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time. (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the `degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller `chaos'), and have their peaks on the increasing GBM exponential. This exponential is thus the `trend of progress' in human history. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra

Brownian motion and stochastic calculus

CERN Document Server

Karatzas, Ioannis

1998-01-01

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...

Uncertainty Reduction for Stochastic Processes on Complex Networks

Science.gov (United States)

Radicchi, Filippo; Castellano, Claudio

2018-05-01

Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the stochastic rules, the ability to predict system configurations is generally characterized by a large uncertainty. Selecting a fraction of the nodes and observing their state may help to reduce the uncertainty about the unobserved nodes. However, choosing these points of observation in an optimal way is a highly nontrivial task, depending on the nature of the stochastic process and on the structure of the underlying interaction pattern. In this paper, we introduce a computationally efficient algorithm to determine quasioptimal solutions to the problem. The method leverages network sparsity to reduce computational complexity from exponential to almost quadratic, thus allowing the straightforward application of the method to mid-to-large-size systems. Although the method is exact only for equilibrium stochastic processes defined on trees, it turns out to be effective also for out-of-equilibrium processes on sparse loopy networks.

Nonlinear stochastic exclusion financial dynamics modeling and time-dependent intrinsic detrended cross-correlation

Science.gov (United States)

Zhang, Wei; Wang, Jun

2017-09-01

In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.

Stochastic volatility and stochastic leverage

DEFF Research Database (Denmark)

Veraart, Almut; Veraart, Luitgard A. M.

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...

Gamma processes and peaks-over-threshold distributions for time-dependent reliability

International Nuclear Information System (INIS)

Noortwijk, J.M. van; Weide, J.A.M. van der; Kallen, M.J.; Pandey, M.D.

2007-01-01

In the evaluation of structural reliability, a failure is defined as the event in which stress exceeds a resistance that is liable to deterioration. This paper presents a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent reliability of a structural component. The deterioration process is modelled as a gamma process, which is a stochastic process with independent non-negative increments having a gamma distribution with identical scale parameter. The stochastic process of loads is generated by a Poisson process. The variability of the random loads is modelled by a peaks-over-threshold distribution (such as the generalised Pareto distribution). These stochastic processes of deterioration and load are combined to evaluate the time-dependent reliability

Selected papers on noise and stochastic processes

CERN Document Server

1954-01-01

Six classic papers on stochastic process, selected to meet the needs of physicists, applied mathematicians, and engineers. Contents: 1.Chandrasekhar, S.: Stochastic Problems in Physics and Astronomy. 2. Uhlenbeck, G. E. and Ornstein, L. S.: On the Theory of the Browninan Motion. 3. Ming Chen Wang and Uhlenbeck, G. E.: On the Theory of the Browninan Motion II. 4. Rice, S. O.: Mathematical Analysis of Random Noise. 5. Kac, Mark: Random Walk and the Theory of Brownian Motion. 6. Doob, J. L.: The Brownian Movement and Stochastic Equations. Unabridged republication of the Dover reprint (1954). Pre

The Application of backward stochastic differential equation with stopping time in hedging American contingent claims

International Nuclear Information System (INIS)

Wang Bo; Song Ruili

2009-01-01

We consider a more general wealth process with a drift coefficient which is Lipschitz continuous and the portfolio process with convex constraint. We convert the problem of hedging American contingent claims into the problem of minimal solution of backward stochastic differential equation with stopping time. We adopt the penalization method for constructing the minimal solution of stochastic differential equations and obtain the upper hedging price of American contingent claims.

Stochastic analysis in production process and ecology under uncertainty

CERN Document Server

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...

Description of quantum-mechanical motion by using the formalism of non-Markov stochastic process

International Nuclear Information System (INIS)

Skorobogatov, G.A.; Svertilov, S.I.

1999-01-01

The principle possibilities of mathematical modeling of quantum mechanical motion by the theory of a real stochastic processes is considered. The set of equations corresponding to the simplest case of a two-level system undergoing transitions under the influence of electromagnetic field are obtained. It is shown that quantum-mechanical processes are purely discrete processes of non-Markovian type. They are continuous processes in the space of probability amplitudes and posses the properties of quantum Markovity. The formulation of quantum mechanics in terms of the theory of stochastic processes is necessary for its generalization on small space-time intervals [ru

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)

Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time

Science.gov (United States)

Dhar, Amrit

2017-01-01

Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780

Distance covariance for stochastic processes

DEFF Research Database (Denmark)

Matsui, Muneya; Mikosch, Thomas Valentin; Samorodnitsky, Gennady

2017-01-01

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analog of the distance covariance for two stochastic processes...

Adaptive control of chaotic systems with stochastic time varying unknown parameters

Energy Technology Data Exchange (ETDEWEB)

Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu

2008-10-15

In this paper based on the Lyapunov stability theorem, an adaptive control scheme is proposed for stabilizing the unstable periodic orbits (UPO) of chaotic systems. It is assumed that the chaotic system has some linearly dependent unknown parameters which are stochastically time varying. The stochastic parameters are modeled through the Weiner process derivative. To demonstrate the effectiveness of the proposed technique it has been applied to the Lorenz, Chen and Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in stabilizing the UPO of chaotic systems in noisy environment.

Stochastic process variation in deep-submicron CMOS circuits and algorithms

CERN Document Server

Zjajo, Amir

2014-01-01

One of the most notable features of nanometer scale CMOS technology is the increasing magnitude of variability of the key device parameters affecting performance of integrated circuits. The growth of variability can be attributed to multiple factors, including the difficulty of manufacturing control, the emergence of new systematic variation-generating mechanisms, and most importantly, the increase in atomic-scale randomness, where device operation must be described as a stochastic process. In addition to wide-sense stationary stochastic device variability and temperature variation, existence of non-stationary stochastic electrical noise associated with fundamental processes in integrated-circuit devices represents an elementary limit on the performance of electronic circuits. In an attempt to address these issues, Stochastic Process Variation in Deep-Submicron CMOS: Circuits and Algorithms offers unique combination of mathematical treatment of random process variation, electrical noise and temperature and ne...

Vehicle routing with stochastic time-dependent travel times

NARCIS (Netherlands)

Lecluyse, C.; Woensel, van T.; Peremans, H.

2009-01-01

Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the

Vehicle routing with stochastic time-dependent travel times

NARCIS (Netherlands)

Lecluyse, C.; Woensel, van T.; Peremans, H.

2007-01-01

Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the

Quantum dynamical time evolutions as stochastic flows on phase space

International Nuclear Information System (INIS)

Combe, P.; Rodriguez, R.; Guerra, F.; Sirigue, M.; Sirigue-Collin, M.

1984-01-01

We are mainly interested in describing the time development of the Wigner functions by means of stochastic processes. In the second section we recall the main properties of the Wigner functions as well as those of their Fourier transform. In the next one we derive the evolution equation of these functions for a class of Hamiltonians and we give a probabilistic expression for the solution of these equations by means of a stochastic flow in phase space which reminds of the classical flows. In the last section we remark that the previously defined flow can be extended to the bounded continuous functions on phase space and that this flow conserves the cone generated by the Wigner functions. (orig./HSI)

Process theory for supervisory control of stochastic systems with data

NARCIS (Netherlands)

Markovski, J.

2012-01-01

We propose a process theory for supervisory control of stochastic nondeterministic plants with data-based observations. The Markovian process theory with data relies on the notion of Markovian partial bisimulation to capture controllability of stochastic nondeterministic systems. It presents a

Visualisation for Stochastic Process Algebras: The Graphic Truth

DEFF Research Database (Denmark)

Smith, Michael James Andrew; Gilmore, Stephen

2011-01-01

and stochastic activity networks provide an automaton-based view of the model, which may be easier to visualise, at the expense of portability. In this paper, we argue that we can achieve the benefits of both approaches by generating a graphical view of a stochastic process algebra model, which is synchronised...

Mapping stochastic processes onto complex networks

International Nuclear Information System (INIS)

Shirazi, A H; Reza Jafari, G; Davoudi, J; Peinke, J; Reza Rahimi Tabar, M; Sahimi, Muhammad

2009-01-01

We introduce a method by which stochastic processes are mapped onto complex networks. As examples, we construct the networks for such time series as those for free-jet and low-temperature helium turbulence, the German stock market index (the DAX), and white noise. The networks are further studied by contrasting their geometrical properties, such as the mean length, diameter, clustering, and average number of connections per node. By comparing the network properties of the original time series investigated with those for the shuffled and surrogate series, we are able to quantify the effect of the long-range correlations and the fatness of the probability distribution functions of the series on the networks constructed. Most importantly, we demonstrate that the time series can be reconstructed with high precision by means of a simple random walk on their corresponding networks

Stationary and related stochastic processes sample function properties and their applications

CERN Document Server

Cramér, Harald

2004-01-01

This graduate-level text offers a comprehensive account of the general theory of stationary processes, with special emphasis on the properties of sample functions. Assuming a familiarity with the basic features of modern probability theory, the text develops the foundations of the general theory of stochastic processes, examines processes with a continuous-time parameter, and applies the general theory to procedures key to the study of stationary processes. Additional topics include analytic properties of the sample functions and the problem of time distribution of the intersections between a

Stochastic time scale for the Universe

International Nuclear Information System (INIS)

Szydlowski, M.; Golda, Z.

1986-01-01

An intrinsic time scale is naturally defined within stochastic gradient dynamical systems. It should be interpreted as a ''relaxation time'' to a local potential minimum after the system has been randomly perturbed. It is shown that for a flat Friedman-like cosmological model this time scale is of order of the age of the Universe. 7 refs. (author)

Relative entropy and waiting time for continuous-time Markov processes

NARCIS (Netherlands)

Chazottes, J.R.; Giardinà, C.; Redig, F.H.J.

2006-01-01

For discrete-time stochastic processes, there is a close connection between return (resp. waiting) times and entropy (resp. relative entropy). Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one needs a reference measure on

Reversibility in Quantum Models of Stochastic Processes

Science.gov (United States)

Gier, David; Crutchfield, James; Mahoney, John; James, Ryan

Natural phenomena such as time series of neural firing, orientation of layers in crystal stacking and successive measurements in spin-systems are inherently probabilistic. The provably minimal classical models of such stochastic processes are ɛ-machines, which consist of internal states, transition probabilities between states and output values. The topological properties of the ɛ-machine for a given process characterize the structure, memory and patterns of that process. However ɛ-machines are often not ideal because their statistical complexity (Cμ) is demonstrably greater than the excess entropy (E) of the processes they represent. Quantum models (q-machines) of the same processes can do better in that their statistical complexity (Cq) obeys the relation Cμ >= Cq >= E. q-machines can be constructed to consider longer lengths of strings, resulting in greater compression. With code-words of sufficiently long length, the statistical complexity becomes time-symmetric - a feature apparently novel to this quantum representation. This result has ramifications for compression of classical information in quantum computing and quantum communication technology.

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)

Stochastic processes in mechanical engineering

NARCIS (Netherlands)

Brouwers, J.J.H.

2006-01-01

Stochastic or random vibrations occur in a variety of applications of mechanicalengineering. Examples are: the dynamics of a vehicle on an irregular roadsurface; the variation in time of thermodynamic variables in municipal wasteincinerators due to fluctuations in heating value of the waste; the

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.

Ranking paths in stochastic time-dependent networks

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele D.

2014-01-01

In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in...

Stochastic nature of series of waiting times

Science.gov (United States)

Anvari, Mehrnaz; Aghamohammadi, Cina; Dashti-Naserabadi, H.; Salehi, E.; Behjat, E.; Qorbani, M.; Khazaei Nezhad, M.; Zirak, M.; Hadjihosseini, Ali; Peinke, Joachim; Tabar, M. Reza Rahimi

2013-06-01

Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the “waiting times” series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2time distribution. We find that the logarithmic difference of waiting times series has a short-range correlation, and then we study its stochastic nature using the Markovian method and determine the corresponding Kramers-Moyal coefficients. As an example, we analyze the velocity fluctuations in high Reynolds number turbulence and determine the level dependence of Markov time scales, as well as the drift and diffusion coefficients. We show that the waiting time distributions exhibit power law tails, and we were able to model the distribution with a continuous time random walk.

Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.

Science.gov (United States)

Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo

2014-07-01

Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs. Copyright © 2014 Elsevier Ltd. All rights reserved.

Towards Model Checking Stochastic Process Algebra

NARCIS (Netherlands)

Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.

2000-01-01

Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of

Stochastic models for structured populations scaling limits and long time behavior

CERN Document Server

Meleard, Sylvie

2015-01-01

In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading  to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of  environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured P...

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.

Stationary distributions of stochastic processes described by a linear neutral delay differential equation

International Nuclear Information System (INIS)

Frank, T D

2005-01-01

Stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation. The distributions are Gaussian distributions. The variances of the Gaussian distributions are either monotonically increasing or decreasing functions of the time delays. The variances become infinite when fixed points of corresponding deterministic processes become unstable. (letter to the editor)

? filtering for stochastic systems driven by Poisson processes

Science.gov (United States)

Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya

2015-01-01

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Gene regulation and noise reduction by coupling of stochastic processes

Science.gov (United States)

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.

Gene regulation and noise reduction by coupling of stochastic processes.

Science.gov (United States)

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 Analysis of Gaussian Processes via Fredholm Representation

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Tommi Sottinen

2016-01-01

Full Text Available We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. We show the convenience of the Fredholm representation by giving applications to equivalence in law, bridges, series expansions, stochastic differential equations, and maximum likelihood estimations.

An extension of clarke's model with stochastic amplitude flip processes

KAUST Repository

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.

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......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 proposed...... for a joint latent factor and show that its inclusion allows for an improved and more parsimonious specification of the multivariate intensity process...

Stochastic behavior of a cold standby system with maximum repair time

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Ashish Kumar

2015-09-01

Full Text Available The main aim of the present paper is to analyze the stochastic behavior of a cold standby system with concept of preventive maintenance, priority and maximum repair time. For this purpose, a stochastic model is developed in which initially one unit is operative and other is kept as cold standby. There is a single server who visits the system immediately as and when required. The server takes the unit under preventive maintenance after a maximum operation time at normal mode if one standby unit is available for operation. If the repair of the failed unit is not possible up to a maximum repair time, failed unit is replaced by new one. The failure time, maximum operation time and maximum repair time distributions of the unit are considered as exponentially distributed while repair and maintenance time distributions are considered as arbitrary. All random variables are statistically independent and repairs are perfect. Various measures of system effectiveness are obtained by using the technique of semi-Markov process and RPT. To highlight the importance of the study numerical results are also obtained for MTSF, availability and profit function.

Classical and spatial stochastic processes with applications to biology

CERN Document Server

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...

The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates

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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.

Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

Science.gov (United States)

Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe

1994-01-01

We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

Science.gov (United States)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

Kinetic theory of age-structured stochastic birth-death processes

Science.gov (United States)

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.

Sliding mode control-based linear functional observers for discrete-time stochastic systems

Science.gov (United States)

Singh, Satnesh; Janardhanan, Sivaramakrishnan

2017-11-01

Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.

Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations

International Nuclear Information System (INIS)

Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George

2016-01-01

The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766–1793 (1996); ibid. 56, 1794–1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.

ON REGRESSION REPRESENTATIONS OF STOCHASTIC-PROCESSES

NARCIS (Netherlands)

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

Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise.

Science.gov (United States)

Chen, Po-Wei; Chen, Bor-Sen

2011-08-01

Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods. Copyright © 2011 Elsevier Inc. All rights reserved.

ℋ∞ constant gain state feedback stabilization of stochastic hybrid systems with Wiener process

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E. K. Boukas

2004-01-01

Full Text Available This paper considers the stabilization problem of the class of continuous-time linear stochastic hybrid systems with Wiener process. The ℋ∞ state feedback stabilization problem is treated. A state feedback controller with constant gain that does not require access to the system mode is designed. LMI-based conditions are developed to design the state feedback controller with constant gain that stochastically stabilizes the studied class of systems and, at the same time, achieve the disturbance rejection of a desired level. The minimum disturbance rejection is also determined. Numerical examples are given to show the usefulness of the proposed results.

Topological superposition of abstractions of stochastic processes

NARCIS (Netherlands)

Bujorianu, L.M.; Bujorianu, M.C.

2008-01-01

In this paper, we present a sound integration mechanism for Markov processes that are abstractions of stochastic hybrid systems (SHS). In a previous work, we have defined a very general model of SHS and we proved that the realization of an SHS is a Markov process. Moreover, we have developed a

Stationary stochastic processes for scientists and engineers

CERN Document Server

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

Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles

Science.gov (United States)

Katsoulakis, Markos A.; Vlachos, Dionisios G.

2003-11-01

We derive a hierarchy of successively coarse-grained stochastic processes and associated coarse-grained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives self-consistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarse-graining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarse-graining in space leads also to coarse-graining in time by q2, where q is the level of coarse-graining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from q3 for short potentials to q4 for long potentials. Finally, connections of the new coarse-grained stochastic processes to stochastic mesoscopic and Cahn-Hilliard-Cook models are made.

A METHODOLOGY FOR THE CHOICE OF THE BEST FITTING CONTINUOUS-TIME STOCHASTIC MODELS OF CRUDE OIL PRICE: THE CASE OF RUSSIA

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Hamidreza Mostafaei

2013-01-01

Full Text Available In this study, it has been attempted to select the best continuous- time stochastic model, in order to describe and forecast the oil price of Russia, by information and statistics about oil price that has been available for oil price in the past. For this purpose, method of The Maximum Likelihood Estimation is implemented for estimation of the parameters of continuous-time stochastic processes. The result of unit root test with a structural break, reveals that time series of the crude oil price is a stationary series. The simulation of continuous-time stochastic processes and the mean square error between the simulated prices and the market ones shows that the Geometric Brownian Motion is the best model for the Russian crude oil price.

Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling

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Rathinasamy Sakthivel

2018-01-01

Full Text Available The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.

Stochastic Landau equation with time-dependent drift

International Nuclear Information System (INIS)

Swift, J.B.; Hohenberg, P.C.; Ahlers, G.

1991-01-01

The stochastic differential equation τ 0 ∂ tA =ε(t)A-g 3 A 3 +bar f(t), where bar f(t) is Gaussian white noise, is studied for arbitrary time dependence of ε(t). In particular, cases are considered where ε(t) goes through the bifurcation of the deterministic system, which occurs at ε=0. In the limit of weak noise an approximate analytic expression generalizing earlier work of Suzuki [Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) Suppl. 64, 402 (1978)] is obtained for the time-dependent distribution function P(A,t). The results compare favorably with a numerical simulation of the stochastic equation for the case of a linear ramp (both increasing and decreasing) and for a periodic time dependence of ε(t). The procedure can be generalized to an arbitrary deterministic part ∂ tA =D(A,t)+bar f(t), but the deterministic equation may then have to be solved numerically

A stochastic surplus production model in continuous time

DEFF Research Database (Denmark)

Pedersen, Martin Wæver; Berg, Casper Willestofte

2017-01-01

surplus production model in continuous time (SPiCT), which in addition to stock dynamics also models the dynamics of the fisheries. This enables error in the catch process to be reflected in the uncertainty of estimated model parameters and management quantities. Benefits of the continuous-time state......Surplus production modelling has a long history as a method for managing data-limited fish stocks. Recent advancements have cast surplus production models as state-space models that separate random variability of stock dynamics from error in observed indices of biomass. We present a stochastic......-space model formulation include the ability to provide estimates of exploitable biomass and fishing mortality at any point in time from data sampled at arbitrary and possibly irregular intervals. We show in a simulation that the ability to analyse subannual data can increase the effective sample size...

Time-dependent solutions for stochastic systems with delays: Perturbation theory and applications to financial physics

International Nuclear Information System (INIS)

Frank, T.D.

2006-01-01

First-order approximations of time-dependent solutions are determined for stochastic systems perturbed by time-delayed feedback forces. To this end, the theory of delay Fokker-Planck equations is applied in combination with Bayes' theorem. Applications to a time-delayed Ornstein-Uhlenbeck process and the geometric Brownian walk of financial physics are discussed

Risk-sensitive control of stochastic hybrid systems on infinite time horizon

Directory of Open Access Journals (Sweden)

Runolfsson Thordur

1999-01-01

Full Text Available A risk-sensitive optimal control problem is considered for a hybrid system that consists of continuous time diffusion process that depends on a discrete valued mode variable that is modeled as a Markov chain. Optimality conditions are presented and conditions for the existence of optimal controls are derived. It is shown that the optimal risk-sensitive control problem is equivalent to the upper value of an associated stochastic differential game, and insight into the contributions of the noise input and mode variable to the risk sensitivity of the cost functional is given. Furthermore, it is shown that due to the mode variable risk sensitivity, the equivalence relationship that has been observed between risk-sensitive and H ∞ control in the nonhybrid case does not hold for stochastic hybrid systems.

Adaptive logical stochastic resonance in time-delayed synthetic genetic networks

Science.gov (United States)

Zhang, Lei; Zheng, Wenbin; Song, Aiguo

2018-04-01

In the paper, the concept of logical stochastic resonance is applied to implement logic operation and latch operation in time-delayed synthetic genetic networks derived from a bacteriophage λ. Clear logic operation and latch operation can be obtained when the network is tuned by modulated periodic force and time-delay. In contrast with the previous synthetic genetic networks based on logical stochastic resonance, the proposed system has two advantages. On one hand, adding modulated periodic force to the background noise can increase the length of the optimal noise plateau of obtaining desired logic response and make the system adapt to varying noise intensity. On the other hand, tuning time-delay can extend the optimal noise plateau to larger range. The result provides possible help for designing new genetic regulatory networks paradigm based on logical stochastic resonance.

A theory of Markovian time-inconsistent stochastic control in discrete time

DEFF Research Database (Denmark)

Bjork, Tomas; Murgoci, Agatha

2014-01-01

We develop a theory for a general class of discrete-time stochastic control problems that, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We attack these problems by viewing them within a game theoretic framework, and we look for subgame...

Quantum stochastic calculus associated with quadratic quantum noises

International Nuclear Information System (INIS)

Ji, Un Cig; Sinha, Kalyan B.

2016-01-01

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus

Quantum stochastic calculus associated with quadratic quantum noises

Energy Technology Data Exchange (ETDEWEB)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

Set-Valued Stochastic Lebesque Integral and Representation Theorems

Directory of Open Access Journals (Sweden)

Jungang Li

2008-06-01

Full Text Available In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection set. After recalling the Aumann type definition of stochastic integral, we shall introduce a new definition of Lebesgue integral of a set-valued stochastic process with respect to the time t . Finally we shall prove the presentation theorem of set-valued stochastic integral and dis- cuss further properties that will be useful to study set-valued stochastic differential equations with their applications.

Stochastic Modelling of Shiroro River Stream flow Process

OpenAIRE

Musa, J. J

2013-01-01

Economists, social scientists and engineers provide insights into the drivers of anthropogenic climate change and the options for adaptation and mitigation, and yet other scientists, including geographers and biologists, study the impacts of climate change. This project concentrates mainly on the discharge from the Shiroro River. A stochastic approach is presented for modeling a time series by an Autoregressive Moving Average model (ARMA). The development and use of a stochastic stream flow m...

H∞ state estimation for discrete-time memristive recurrent neural networks with stochastic time-delays

Science.gov (United States)

Liu, Hongjian; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.

2016-07-01

This paper deals with the robust H∞ state estimation problem for a class of memristive recurrent neural networks with stochastic time-delays. The stochastic time-delays under consideration are governed by a Bernoulli-distributed stochastic sequence. The purpose of the addressed problem is to design the robust state estimator such that the dynamics of the estimation error is exponentially stable in the mean square, and the prescribed ? performance constraint is met. By utilizing the difference inclusion theory and choosing a proper Lyapunov-Krasovskii functional, the existence condition of the desired estimator is derived. Based on it, the explicit expression of the estimator gain is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is employed to demonstrate the effectiveness and applicability of the proposed estimation approach.

Stochastic formalism-based seafloor feature discrimination using multifractality of time-dependent acoustic backscatter

Digital Repository Service at National Institute of Oceanography (India)

Haris, K.; Chakraborty, B.

Nonlin. Processes Geophys., 21, 101–113, 2014 www.nonlin-processes-geophys.net/21/101/2014/ doi:10.5194/npg-21-101-2014 © Author(s) 2014. CC Attribution 3.0 License. Nonlinear Processes in Geophysics O pen A ccess Stochastic formalism-based seafloor... shifted in time to align with the selected feature (Fig. 2). The aligned echo envelopes were averaged to obtain stable acoustic signals to Nonlin. Processes Geophys., 21, 101–113, 2014 www.nonlin-processes-geophys.net/21/101/2014/ K. Haris and B...

Stochastic Modelling Of The Repairable System

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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.

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...

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.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

Energy Technology Data Exchange (ETDEWEB)

Yu, Haitao; Guo, Xinmeng; Wang, Jiang, E-mail: jiangwang@tju.edu.cn; Deng, Bin; Wei, Xile [School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072 (China)

2014-09-01

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

International Nuclear Information System (INIS)

Yu, Haitao; Guo, Xinmeng; Wang, Jiang; Deng, Bin; Wei, Xile

2014-01-01

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks

First-Passage-Time Distribution for Variable-Diffusion Processes

Science.gov (United States)

Barney, Liberty; Gunaratne, Gemunu H.

2017-05-01

First-passage-time distribution, which presents the likelihood of a stock reaching a pre-specified price at a given time, is useful in establishing the value of financial instruments and in designing trading strategies. First-passage-time distribution for Wiener processes has a single peak, while that for stocks exhibits a notable second peak within a trading day. This feature has only been discussed sporadically—often dismissed as due to insufficient/incorrect data or circumvented by conversion to tick time—and to the best of our knowledge has not been explained in terms of the underlying stochastic process. It was shown previously that intra-day variations in the market can be modeled by a stochastic process containing two variable-diffusion processes (Hua et al. in, Physica A 419:221-233, 2015). We show here that the first-passage-time distribution of this two-stage variable-diffusion model does exhibit a behavior similar to the empirical observation. In addition, we find that an extended model incorporating overnight price fluctuations exhibits intra- and inter-day behavior similar to those of empirical first-passage-time distributions.

Solving Langevin equation with the stochastic algebraically correlated noise

International Nuclear Information System (INIS)

Ploszajczak, M.; Srokowski, T.

1996-01-01

Long time tail in the velocity and force autocorrelation function has been found recently in the molecular dynamics simulations of the peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. The Markovian process and the multidimensional Kangaroo process which permit describing various algebraic correlated stochastic processes are proposed. (author)

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)

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.

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)

Stochastic first passage time accelerated with CUDA

Science.gov (United States)

Pierro, Vincenzo; Troiano, Luigi; Mejuto, Elena; Filatrella, Giovanni

2018-05-01

The numerical integration of stochastic trajectories to estimate the time to pass a threshold is an interesting physical quantity, for instance in Josephson junctions and atomic force microscopy, where the full trajectory is not accessible. We propose an algorithm suitable for efficient implementation on graphical processing unit in CUDA environment. The proposed approach for well balanced loads achieves almost perfect scaling with the number of available threads and processors, and allows an acceleration of about 400× with a GPU GTX980 respect to standard multicore CPU. This method allows with off the shell GPU to challenge problems that are otherwise prohibitive, as thermal activation in slowly tilted potentials. In particular, we demonstrate that it is possible to simulate the switching currents distributions of Josephson junctions in the timescale of actual experiments.

Stochastic fractional differential equations: Modeling, method and analysis

International Nuclear Information System (INIS)

Pedjeu, Jean-C.; Ladde, Gangaram S.

2012-01-01

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.

Time-adaptive and history-adaptive multicriterion routing in stochastic, time-dependent networks

DEFF Research Database (Denmark)

Pretolani, Daniele; Nielsen, Lars Relund; Andersen, Kim Allan

2009-01-01

We compare two different models for multicriterion routing in stochastic time-dependent networks: the classic "time-adaptive'' model and the more flexible "history-adaptive'' one. We point out several properties of the sets of efficient solutions found under the two models. We also devise a method...

Exponential stability of uncertain stochastic neural networks with mixed time-delays

International Nuclear Information System (INIS)

Wang Zidong; Lauria, Stanislao; Fang Jian'an; Liu Xiaohui

2007-01-01

This paper is concerned with the global exponential stability analysis problem for a class of stochastic neural networks with mixed time-delays and parameter uncertainties. The mixed delays comprise discrete and distributed time-delays, the parameter uncertainties are norm-bounded, and the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion. The purpose of the stability analysis problem is to derive easy-to-test criteria under which the delayed stochastic neural network is globally, robustly, exponentially stable in the mean square for all admissible parameter uncertainties. By resorting to the Lyapunov-Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established by using an efficient linear matrix inequality (LMI) approach. The proposed criteria can be checked readily by using recently developed numerical packages, where no tuning of parameters is required. An example is provided to demonstrate the usefulness of the proposed criteria

Fixation and escape times in stochastic game learning

International Nuclear Information System (INIS)

Realpe-Gomez, John; Szczesny, Bartosz; Galla, Tobias; Dall’Asta, Luca

2012-01-01

Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning processes in a simple 2×2 game, for two-player games with cyclic interaction, and in the context of the best-shot network game. The analogues of finite populations in evolution are here finite batches of observations between strategy updates. We study when and how such fixation can occur, and present results on the average time-to-fixation from numerical simulations. Simple cases are also amenable to analytical approaches and we provide estimates of the behaviour of so-called escape times as a function of the batch size. The differences and similarities with escape and fixation in evolutionary dynamics are discussed. (paper)

A Fractionally Integrated Wishart Stochastic Volatility Model

NARCIS (Netherlands)

M. Asai (Manabu); M.J. McAleer (Michael)

2013-01-01

textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of

XI Symposium on Probability and Stochastic Processes

CERN Document Server

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...

Probability, Statistics, and Stochastic Processes

CERN Document Server

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 processes and filtering theory

CERN Document Server

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

Stochastic modeling and analysis of telecoms networks

CERN Document Server

Decreusefond, Laurent

2012-01-01

This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an

Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

International Nuclear Information System (INIS)

Yong-Feng, Guo; Wei, Xu; Liang, Wang

2010-01-01

This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker–Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time τ on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears. (general)

Stochastic temperature and the Nicolai map

International Nuclear Information System (INIS)

Hueffel, H.

1989-01-01

Just as standard temperature can be related to the time coordinate of Euclidean space, a new concept of 'stochastic temperature' may be introduced by associating it to the Parisi-Wu time of stochastic quantization. The perturbative equilibrium limit for a self-interacting scalar field is studied, and a 'thermal' mass shift to one loop is shown. In addition one may interpret the underlying stochastic process as a Nicolai map at nonzero 'temperature'. 22 refs. (Author)

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model

Science.gov (United States)

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.

Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach

International Nuclear Information System (INIS)

Ferrari, Giorgio; Riedel, Frank; Steg, Jan-Henrik

2017-01-01

In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochastic Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.

Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach

Energy Technology Data Exchange (ETDEWEB)

Ferrari, Giorgio, E-mail: giorgio.ferrari@uni-bielefeld.de; Riedel, Frank, E-mail: frank.riedel@uni-bielefeld.de; Steg, Jan-Henrik, E-mail: jsteg@uni-bielefeld.de [Bielefeld University, Center for Mathematical Economics (Germany)

2017-06-15

In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochastic Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.

Stochastic Averaging and Stochastic Extremum Seeking

CERN Document Server

Liu, Shu-Jun

2012-01-01

Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering  and analysis of bacterial  convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...

Exact norm-conserving stochastic time-dependent Hartree-Fock

International Nuclear Information System (INIS)

Tessieri, Luca; Wilkie, Joshua; Cetinbas, Murat

2005-01-01

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method, we calculate the low energy spectrum of helium. An extension of the method to bosons is outlined

Reliability and maintenance in European nuclear power plants: A structural analysis of a controlled stochastic process

International Nuclear Information System (INIS)

Sturm, R.

1991-01-01

Two aspects of performance are of main concern: plant availability and plant reliability (defined as the conditional probability of an unplanned shutdown). The goal of the research is a unified framework that combines behavioral models of optimizing agents with models of complex technical systems that take into account the dynamic and stochastic features of the system. In order to achieve this synthesis, two liens of work are necessary. One line requires a deeper understanding of complex production systems and the type of data they give rise to; the other line involves the specification and estimation of a rigorously specified behavioral model. Plant operations are modeled as a controlled stochastic process, and the sequence of up and downtime spells is analyzed during failure time and point process models. Similar to work on rational expectations and structural econometric models, the behavior model of how the plant process is controlled is formulated at the level of basic processes, i.e., the objective function of the plant manager, technical constraints, and stochastic disturbances

Stochastic quantization and topological theories

International Nuclear Information System (INIS)

Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.

1992-01-01

In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones

Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework

International Nuclear Information System (INIS)

Zhou, X.Y.; Li, D.

2000-01-01

This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be 'embedded' into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem

Quantum stochastics

CERN Document Server

Chang, Mou-Hsiung

2015-01-01

The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...

Stochastic light-cone CTMRG: a new DMRG approach to stochastic models 02.50.Ey Stochastic processes; 64.60.Ht Dynamic critical phenomena; 02.70.-c Computational techniques; 05.10.Cc Renormalization group methods;

CERN Document Server

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.

Event-Triggered Faults Tolerant Control for Stochastic Systems with Time Delays

Directory of Open Access Journals (Sweden)

Ling Huang

2016-01-01

Full Text Available This paper is concerned with the state-feedback controller design for stochastic networked control systems (NCSs with random actuator failures and transmission delays. Firstly, an event-triggered scheme is introduced to optimize the performance of the stochastic NCSs. Secondly, stochastic NCSs under event-triggered scheme are modeled as stochastic time-delay systems. Thirdly, some less conservative delay-dependent stability criteria in terms of linear matrix inequalities for the codesign of both the controller gain and the trigger parameters are obtained by using delay-decomposition technique and convex combination approach. Finally, a numerical example is provided to show the less sampled data transmission and less conservatism of the proposed theory.

Single-molecule stochastic times in a reversible bimolecular reaction

Science.gov (United States)

Keller, Peter; Valleriani, Angelo

2012-08-01

In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.

Phenomenological and ratio bifurcations of a class of discrete time stochastic processes

NARCIS (Netherlands)

Diks, C.G.H.; Wagener, F.O.O.

2011-01-01

Zeeman proposed a classification of stochastic dynamical systems based on the Morse classification of their invariant probability densities; the associated bifurcations are the ‘phenomenological bifurcations’ of L. Arnold. The classification is however not invariant under diffeomorphisms of the

Stochastic time-dependent vehicle routing problem: Mathematical models and ant colony algorithm

Directory of Open Access Journals (Sweden)

Zhengyu Duan

2015-11-01

Full Text Available This article addresses the stochastic time-dependent vehicle routing problem. Two mathematical models named robust optimal schedule time model and minimum expected schedule time model are proposed for stochastic time-dependent vehicle routing problem, which can guarantee delivery within the time windows of customers. The robust optimal schedule time model only requires the variation range of link travel time, which can be conveniently derived from historical traffic data. In addition, the robust optimal schedule time model based on robust optimization method can be converted into a time-dependent vehicle routing problem. Moreover, an ant colony optimization algorithm is designed to solve stochastic time-dependent vehicle routing problem. As the improvements in initial solution and transition probability, ant colony optimization algorithm has a good performance in convergence. Through computational instances and Monte Carlo simulation tests, robust optimal schedule time model is proved to be better than minimum expected schedule time model in computational efficiency and coping with the travel time fluctuations. Therefore, robust optimal schedule time model is applicable in real road network.

Stochastic inflation as a time-dependent random walk

International Nuclear Information System (INIS)

Kandrup, H.E.

1989-01-01

This paper exploits the ''stochastic inflation'' paradigm introduced by Starobinskii to study the evolution of long-wavelength modes for a free scalar field Phi in an inflationary Universe. By relaxing the assumption of a ''slow roll,'' it becomes obvious that the well-known late-time infrared divergence of the vacuum for a massless field in de Sitter space may be viewed as a consequence of the fluctuation-dissipation theorem. This stochastic model is also extended to allow for nonvacuum states and power-law inflation, situations where the fluctuation-dissipation theorem no longer holds. One recovers the correct late-time form for the expectation value 2 > in these cases as well, corroborating thereby the intuitive picture that, quite generally, the long-wavelength modes of the field evolve in a thermal ''bath'' provided by the shorter-wavelength modes

Stochastic processes, multiscale modeling, and numerical methods for computational cellular biology

CERN Document Server

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...

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

Science.gov (United States)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

Science.gov (United States)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Simulating biological processes: stochastic physics from whole cells to colonies

Science.gov (United States)

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 analysis of biochemical systems

CERN Document Server

Anderson, David F

2015-01-01

This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology.  The book should serve well as a supplement for courses in probability and stochastic processes.  While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations, and elementary probability and who are well-motivated by the applications will find this book of interest.    David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other ar...

Transport properties of stochastic Lorentz models

NARCIS (Netherlands)

Beijeren, H. van

Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed

Modeling spiking behavior of neurons with time-dependent Poisson processes.

Science.gov (United States)

Shinomoto, S; Tsubo, Y

2001-10-01

Three kinds of interval statistics, as represented by the coefficient of variation, the skewness coefficient, and the correlation coefficient of consecutive intervals, are evaluated for three kinds of time-dependent Poisson processes: pulse regulated, sinusoidally regulated, and doubly stochastic. Among these three processes, the sinusoidally regulated and doubly stochastic Poisson processes, in the case when the spike rate varies slowly compared with the mean interval between spikes, are found to be consistent with the three statistical coefficients exhibited by data recorded from neurons in the prefrontal cortex of monkeys.

Adaptive Asymptotical Synchronization for Stochastic Complex Networks with Time-Delay and Markovian Switching

Directory of Open Access Journals (Sweden)

Xueling Jiang

2014-01-01

Full Text Available The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and the M-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.

Existence of time-periodic weak solutions to the stochastic Navier-Stokes equations around a moving body

International Nuclear Information System (INIS)

Chen, Feng; Han, Yuecai

2013-01-01

The existence of time-periodic stochastic motions of an incompressible fluid is obtained. Here the fluid is subject to a time-periodic body force and an additional time-periodic stochastic force that is produced by a rigid body moves periodically stochastically with the same period in the fluid

Existence of time-periodic weak solutions to the stochastic Navier-Stokes equations around a moving body

Energy Technology Data Exchange (ETDEWEB)

Chen, Feng, E-mail: chenfengmath@163.com, E-mail: hanyc@jlu.edu.cn; Han, Yuecai, E-mail: chenfengmath@163.com, E-mail: hanyc@jlu.edu.cn [School of Mathematics, Jilin University, Changchun 130012 (China)

2013-12-15

The existence of time-periodic stochastic motions of an incompressible fluid is obtained. Here the fluid is subject to a time-periodic body force and an additional time-periodic stochastic force that is produced by a rigid body moves periodically stochastically with the same period in the fluid.

Statistical Methods for Stochastic Differential Equations

CERN Document Server

Kessler, Mathieu; Sorensen, Michael

2012-01-01

The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp

Entropy Production in Stochastics

Directory of Open Access Journals (Sweden)

Demetris Koutsoyiannis

2017-10-01

Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

Science.gov (United States)

Schilde, M; Doerner, K F; Hartl, R F

2014-10-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays

Directory of Open Access Journals (Sweden)

Manlika Rajchakit

2012-01-01

Full Text Available This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.

Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator

Science.gov (United States)

González Ochoa, Héctor O.; Perales, Gualberto Solís; Epstein, Irving R.; Femat, Ricardo

2018-05-01

We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.

Continuous strong Markov processes in dimension one a stochastic calculus approach

CERN Document Server

Assing, Sigurd

1998-01-01

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

Science.gov (United States)

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Conditional Stochastic Processes Applied to Wave Load Predictions

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2015-01-01

The concept of conditional stochastic processes provides a powerful tool for evaluation and estimation of wave loads on ships and offshore structures. This article first considers conditional waves with a focus on critical wave episodes. Then the inherent uncertainty in the results is illustrated...

Modeling and analysis of stochastic systems

CERN Document Server

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

Optimal timing of joint replacement using mathematical programming and stochastic programming models.

Science.gov (United States)

Keren, Baruch; Pliskin, Joseph S

2011-12-01

The optimal timing for performing radical medical procedures as joint (e.g., hip) replacement must be seriously considered. In this paper we show that under deterministic assumptions the optimal timing for joint replacement is a solution of a mathematical programming problem, and under stochastic assumptions the optimal timing can be formulated as a stochastic programming problem. We formulate deterministic and stochastic models that can serve as decision support tools. The results show that the benefit from joint replacement surgery is heavily dependent on timing. Moreover, for a special case where the patient's remaining life is normally distributed along with a normally distributed survival of the new joint, the expected benefit function from surgery is completely solved. This enables practitioners to draw the expected benefit graph, to find the optimal timing, to evaluate the benefit for each patient, to set priorities among patients and to decide if joint replacement should be performed and when.

An effective streamflow process model for optimal reservoir operation using stochastic dual dynamic programming

OpenAIRE

Raso , L.; Malaterre , P.O.; Bader , J.C.

2017-01-01

International audience; This article presents an innovative streamflow process model for use in reservoir operational rule design in stochastic dual dynamic programming (SDDP). Model features, which can be applied independently, are (1) a multiplicative process model for the forward phase and its linearized version for the backward phase; and (2) a nonuniform time-step length that is inversely proportional to seasonal variability. The advantages are (1) guaranteeing positive streamflow values...

Stochastic Power Control for Time-Varying Long-Term Fading Wireless Networks

Directory of Open Access Journals (Sweden)

Charalambous Charalambos D

2006-01-01

Full Text Available A new time-varying (TV long-term fading (LTF channel model which captures both the space and time variations of wireless systems is developed. The proposed TV LTF model is based on a stochastic differential equation driven by Brownian motion. This model is more realistic than the static models usually encountered in the literature. It allows viewing the wireless channel as a dynamical system, thus enabling well-developed tools of adaptive and nonadaptive estimation and identification techniques to be applied to this class of problems. In contrast with the traditional models, the statistics of the proposed model are shown to be TV, but converge in steady state to their static counterparts. Moreover, optimal power control algorithms (PCAs based on the new model are proposed. A centralized PCA is shown to reduce to a simple linear programming problem if predictable power control strategies (PPCS are used. In addition, an iterative distributed stochastic PCA is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal-to-interference ratio. Generalizations of the power control problem based on convex optimization techniques are provided if PPCS are not assumed. Numerical results show that there are potentially large gains to be achieved by using TV stochastic models, and the distributed stochastic PCA provides better power stability and consumption than the distributed deterministic PCA.

5th Seminar on Stochastic Processes, Random Fields and Applications

CERN Document Server

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...

Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

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Jie Ran

2015-01-01

Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.

Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection

Directory of Open Access Journals (Sweden)

Gabriel Martos

2018-01-01

Full Text Available We propose a definition of entropy for stochastic processes. We provide a reproducing kernel Hilbert space model to estimate entropy from a random sample of realizations of a stochastic process, namely functional data, and introduce two approaches to estimate minimum entropy sets. These sets are relevant to detect anomalous or outlier functional data. A numerical experiment illustrates the performance of the proposed method; in addition, we conduct an analysis of mortality rate curves as an interesting application in a real-data context to explore functional anomaly detection.

A comparison of the stochastic and machine learning approaches in hydrologic time series forecasting

Science.gov (United States)

Kim, T.; Joo, K.; Seo, J.; Heo, J. H.

2016-12-01

Hydrologic time series forecasting is an essential task in water resources management and it becomes more difficult due to the complexity of runoff process. Traditional stochastic models such as ARIMA family has been used as a standard approach in time series modeling and forecasting of hydrological variables. Due to the nonlinearity in hydrologic time series data, machine learning approaches has been studied with the advantage of discovering relevant features in a nonlinear relation among variables. This study aims to compare the predictability between the traditional stochastic model and the machine learning approach. Seasonal ARIMA model was used as the traditional time series model, and Random Forest model which consists of decision tree and ensemble method using multiple predictor approach was applied as the machine learning approach. In the application, monthly inflow data from 1986 to 2015 of Chungju dam in South Korea were used for modeling and forecasting. In order to evaluate the performances of the used models, one step ahead and multi-step ahead forecasting was applied. Root mean squared error and mean absolute error of two models were compared.

Introduction to Stochastic Simulations for Chemical and Physical Processes: Principles and Applications

Science.gov (United States)

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…

StochPy: A Comprehensive, User-Friendly Tool for Simulating Stochastic Biological Processes

NARCIS (Netherlands)

T.R. Maarleveld (Timo); B.G. Olivier (Brett); F.J. Bruggeman (Frank)

2013-01-01

htmlabstractSingle-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

Quantum mechanics, stochasticity and space-time

International Nuclear Information System (INIS)

Ramanathan, R.

1986-04-01

An extended and more rigorous version of a recent proposal for an objective stochastic formulation of quantum mechanics along with its extension to the relativistic case without spin is presented. The relativistic Klein-Gordon equation is shown to be a particular form of the relativistic Kolmogorov-Fokker-Planck equation which is derived from a covariant formulation of the Chapman-Kolmogorov condition. Complexification of probability amplitudes is again achieved only through a conformal rotation of Minkowski space-time M 4 . (author)

Identification of the structure parameters using short-time non-stationary stochastic excitation

Science.gov (United States)

Jarczewska, Kamila; Koszela, Piotr; Śniady, PaweŁ; Korzec, Aleksandra

2011-07-01

In this paper, we propose an approach to the flexural stiffness or eigenvalue frequency identification of a linear structure using a non-stationary stochastic excitation process. The idea of the proposed approach lies within time domain input-output methods. The proposed method is based on transforming the dynamical problem into a static one by integrating the input and the output signals. The output signal is the structure reaction, i.e. structure displacements due to the short-time, irregular load of random type. The systems with single and multiple degrees of freedom, as well as continuous systems are considered.

Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory

International Nuclear Information System (INIS)

Qian, Hong

2011-01-01

The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

Science.gov (United States)

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

Heuristic for Stochastic Online Flowshop Problem with Preemption Penalties

Directory of Open Access Journals (Sweden)

Mohammad Bayat

2013-01-01

Full Text Available The deterministic flowshop model is one of the most widely studied problems; whereas its stochastic equivalent has remained a challenge. Furthermore, the preemptive online stochastic flowshop problem has received much less attention, and most of the previous researches have considered a nonpreemptive version. Moreover, little attention has been devoted to the problems where a certain time penalty is incurred when preemption is allowed. This paper examines the preemptive stochastic online flowshop with the objective of minimizing the expected makespan. All the jobs arrive overtime, which means that the existence and the parameters of each job are unknown until its release date. The processing time of the jobs is stochastic and actual processing time is unknown until completion of the job. A heuristic procedure for this problem is presented, which is applicable whenever the job processing times are characterized by their means and standard deviation. The performance of the proposed heuristic method is explored using some numerical examples.

Stochastic differential equations and diffusion processes

CERN Document Server

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

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...

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.

Time change

DEFF Research Database (Denmark)

Veraart, Almut; Winkel, Matthias

2010-01-01

The mathematical operation of time-changing continuous-time stochastic processes can be regarded as a standard method for building financial models. We briefly review the theory on time-changed stochastic processes and relate them to stochastic volatility models in finance. Popular models......, including time-changed Lévy processes, where the time-change process is given by a subordinator or an absolutely continuous time change, are presented. Finally, we discuss the potential and the limitations of using such processes for constructing multivariate financial models....

The Ising Decision Maker: a binary stochastic network for choice response time.

Science.gov (United States)

Verdonck, Stijn; Tuerlinckx, Francis

2014-07-01

The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (c) 2014 APA, all rights reserved.

Analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times

Science.gov (United States)

Sharma, Pankaj; Jain, Ajai

2014-12-01

Stochastic dynamic job shop scheduling problem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under due date tightness factor of 3, shop utilization percentage of 90% and setup times less than processing times. Results indicate that shortest setup time (SIMSET) rule provides the best performance for mean flow time and number of tardy jobs measures. The job with similar setup and modified earliest due date (JMEDD) rule provides the best performance for makespan, maximum flow time, mean tardiness, maximum tardiness, total setups and mean setup time measures.

Critical spare parts ordering decisions using conditional reliability and stochastic lead time

International Nuclear Information System (INIS)

Godoy, David R.; Pascual, Rodrigo; Knights, Peter

2013-01-01

Asset-intensive companies face great pressure to reduce operation costs and increase utilization. This scenario often leads to over-stress on critical equipment and its spare parts associated, affecting availability, reliability, and system performance. As these resources impact considerably on financial and operational structures, the opportunity is given by demand for decision-making methods for the management of spare parts processes. We proposed an ordering decision-aid technique which uses a measurement of spare performance, based on the stress–strength interference theory; which we have called Condition-Based Service Level (CBSL). We focus on Condition Managed Critical Spares (CMS), namely, spares which are expensive, highly reliable, with higher lead times, and are not available in store. As a mitigation measure, CMS are under condition monitoring. The aim of the paper is orienting the decision time for CMS ordering or just continuing the operation. The paper presents a graphic technique which considers a rule for decision based on both condition-based reliability function and a stochastic/fixed lead time. For the stochastic lead time case, results show that technique is effective to determine the time when the system operation is reliable and can withstand the lead time variability, satisfying a desired service level. Additionally, for the constant lead time case, the technique helps to define insurance spares. In conclusion, presented ordering decision rule is useful to asset managers for enhancing the operational continuity affected by spare parts

Stochastic stability of mechanical systems under renewal jump process parametric excitation

DEFF Research Database (Denmark)

Iwankiewicz, R.; Nielsen, Søren R.K.; Larsen, Jesper Winther

2005-01-01

independent, negative exponential distributed variables; hence, the arrival process may be termed as a generalized Erlang renewal process. The excitation process is governed by the stochastic equation driven by two independent Poisson processes, with different parameters. If the response in a single mode...

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

Science.gov (United States)

Wang, Jun-Sheng; Yang, Guang-Hong

2017-07-25

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

Partial Finite-Time Synchronization of Switched Stochastic Chua's Circuits via Sliding-Mode Control

Directory of Open Access Journals (Sweden)

Zhang-Lin Wan

2011-01-01

Full Text Available This paper considers the problem of partial finite-time synchronization between switched stochastic Chua's circuits accompanied by a time-driven switching law. Based on the Ito formula and Lyapunov stability theory, a sliding-mode controller is developed to guarantee the synchronization of switched stochastic master-slave Chua's circuits and for the mean of error states to obtain the partial finite-time stability. Numerical simulations demonstrate the effectiveness of the proposed methods.

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

Science.gov (United States)

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.

Continuous stochastic approach to birth and death processes and co-operative behaviour of systems far from equilibrium

Energy Technology Data Exchange (ETDEWEB)

Chechetkin, V.R.; Lutovinov, V.S.

1986-09-11

The continuous stochastic formalism for the description of systems with birth and death processes randomly distributed in space is developed with the use of local birth and death operators and local generalization of the corresponding Chapman-Kolmogorov equation. The functional stochastic equation for the evolution of the probability functional is derived and its modifications for evolution of the characteristic functional and the first passage time problem are given. The corresponding evolution equations for equal-time correlators are also derived. The results are generalized then on the exothermic and endothermic chemical reactions. As examples of the particular applications of the results the small fluctuations near stable equilibrium state and fluctuations in mono-molecular reactions, Lotka-Volterra model, Schloegl reaction and brusselator are considered. It is shown that the two-dimensional Lotka-Volterra model may exhibit synergetic phase transition analogous to the topological transition of the Kosterlitz-Thouless-Berezinskii type. At the end of the paper some general consequences from stochastic evolution of the birth and death processes are discussed and the arguments on their importance in evolution of populations, cellular dynamics and in applications to various chemical and biological problems are presented.

Perturbation theory for continuous stochastic equations

International Nuclear Information System (INIS)

Chechetkin, V.R.; Lutovinov, V.S.

1987-01-01

The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

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...

Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009

Directory of Open Access Journals (Sweden)

Nishiura Hiroshi

2011-02-01

Full Text Available Abstract Background Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. Methods A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009 in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. Results The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Conclusions Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays

Science.gov (United States)

Syed Ali, M.; Balasubramaniam, P.

2008-07-01

In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB.

Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays

International Nuclear Information System (INIS)

Syed Ali, M.; Balasubramaniam, P.

2008-01-01

In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB

Stochastic modeling of neurobiological time series: Power, coherence, Granger causality, and separation of evoked responses from ongoing activity

Science.gov (United States)

Chen, Yonghong; Bressler, Steven L.; Knuth, Kevin H.; Truccolo, Wilson A.; Ding, Mingzhou

2006-06-01

In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis. After subtracting out the event-related signal from recorded single trial time series, the residual ongoing activity is treated as a piecewise stationary stochastic process and analyzed by an adaptive multivariate autoregressive modeling strategy which yields power, coherence, and Granger causality spectra. Results from applying these methods to local field potential recordings from monkeys performing cognitive tasks are presented.

A stochastic fractional dynamics model of space-time variability of rain

Science.gov (United States)

Kundu, Prasun K.; Travis, James E.

2013-09-01

varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.

Robustness Analysis of Hybrid Stochastic Neural Networks with Neutral Terms and Time-Varying Delays

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Chunmei Wu

2015-01-01

Full Text Available We analyze the robustness of global exponential stability of hybrid stochastic neural networks subject to neutral terms and time-varying delays simultaneously. Given globally exponentially stable hybrid stochastic neural networks, we characterize the upper bounds of contraction coefficients of neutral terms and time-varying delays by using the transcendental equation. Moreover, we prove theoretically that, for any globally exponentially stable hybrid stochastic neural networks, if additive neutral terms and time-varying delays are smaller than the upper bounds arrived, then the perturbed neural networks are guaranteed to also be globally exponentially stable. Finally, a numerical simulation example is given to illustrate the presented criteria.

Renormalization in the stochastic quantization of field theories

International Nuclear Information System (INIS)

Brunelli, J.C.

1991-01-01

In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)

H∞ state estimation of stochastic memristor-based neural networks with time-varying delays.

Science.gov (United States)

Bao, Haibo; Cao, Jinde; Kurths, Jürgen; Alsaedi, Ahmed; Ahmad, Bashir

2018-03-01

This paper addresses the problem of H ∞ state estimation for a class of stochastic memristor-based neural networks with time-varying delays. Under the framework of Filippov solution, the stochastic memristor-based neural networks are transformed into systems with interval parameters. The present paper is the first to investigate the H ∞ state estimation problem for continuous-time Itô-type stochastic memristor-based neural networks. By means of Lyapunov functionals and some stochastic technique, sufficient conditions are derived to ensure that the estimation error system is asymptotically stable in the mean square with a prescribed H ∞ performance. An explicit expression of the state estimator gain is given in terms of linear matrix inequalities (LMIs). Compared with other results, our results reduce control gain and control cost effectively. Finally, numerical simulations are provided to demonstrate the efficiency of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Stochastic beam dynamics in storage rings

International Nuclear Information System (INIS)

Pauluhn, A.

1993-12-01

In this thesis several approaches to stochastic dynamics in storage rings are investigated. In the first part the theory of stochastic differential equations and Fokker-Planck equations is used to describe the processes which have been assumed to be Markov processes. The mathematical theory of Markov processes is well known. Nevertheless, analytical solutions can be found only in special cases and numerical algorithms are required. Several numerical integration schemes for stochastic differential equations will therefore be tested in analytical solvable examples and then applied to examples from accelerator physics. In particular the stochastically perturbed synchrotron motion is treated. For the special case of a double rf system several perturbation theoretical methods for deriving the Fokker-Planck equation in the action variable are used and compared with numerical results. The second part is concerned with the dynamics of electron storage rings. Due to the synchrotron radiation the electron motion is influenced by damping and exciting forces. An algorithm for the computation of the density function in the phase space of such a dissipative stochastically excited system is introduced. The density function contains all information of a process, e.g. it determines the beam dimensions and the lifetime of a stored electron beam. The new algorithm consists in calculating a time propagator for the density function. By means of this propagator the time evolution of the density is modelled very computing time efficient. The method is applied to simple models of the beam-beam interaction (one-dimensional, round beams) and the results of the density calculations are compared with results obtained from multiparticle tracking. Furthermore some modifications of the algorithm are introduced to improve its efficiency concerning computing time and storage requirements. Finally, extensions to two-dimensional beam-beam models are described. (orig.)

An Optogenetic Platform for Real-Time, Single-Cell Interrogation of Stochastic Transcriptional Regulation.

Science.gov (United States)

Rullan, Marc; Benzinger, Dirk; Schmidt, Gregor W; Milias-Argeitis, Andreas; Khammash, Mustafa

2018-05-17

Transcription is a highly regulated and inherently stochastic process. The complexity of signal transduction and gene regulation makes it challenging to analyze how the dynamic activity of transcriptional regulators affects stochastic transcription. By combining a fast-acting, photo-regulatable transcription factor with nascent RNA quantification in live cells and an experimental setup for precise spatiotemporal delivery of light inputs, we constructed a platform for the real-time, single-cell interrogation of transcription in Saccharomyces cerevisiae. We show that transcriptional activation and deactivation are fast and memoryless. By analyzing the temporal activity of individual cells, we found that transcription occurs in bursts, whose duration and timing are modulated by transcription factor activity. Using our platform, we regulated transcription via light-driven feedback loops at the single-cell level. Feedback markedly reduced cell-to-cell variability and led to qualitative differences in cellular transcriptional dynamics. Our platform establishes a flexible method for studying transcriptional dynamics in single cells. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

A measure theoretical approach to quantum stochastic processes

CERN Document Server

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.

Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

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Mingzhu Song

2016-01-01

Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

Stochastic quantization of geometrodynamic curved space-time

International Nuclear Information System (INIS)

Prugovecki, E.

1981-01-01

It is proposed that quantum rather than classical test particles be used in recent operational definitions of space-time. In the resulting quantum space-time the role of test particle trajectories is taken over by propagators. The introduced co-ordinate values are stochastic rather than deterministic, the afore-mentioned propagators providing probability amplitudes describing fluctuations of measured co-ordinates around their mean values. It is shown that, if a geometrodynamic point of view based on 3 + 1 foliations of space-time is adopted, self-consistent families of propagators for quantum test particles in free fall can be constructed. The resulting formalism for quantum space-time is outlined and the quantization of spatially flat Robertson-Walker space-times is provided as an illustration. (author)

A first course in stochastic processes

CERN Document Server

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

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

2016-02-15

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

Introduction to modeling and analysis of stochastic systems

CERN Document Server

Kulkarni, V G

2011-01-01

This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany...

Stochastic Analysis 2010

CERN Document Server

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

Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method.

Science.gov (United States)

Zhang, Tingting; Kou, S C

2010-01-01

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.

American option pricing with stochastic volatility processes

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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.

A Family of Poisson Processes for Use in Stochastic Models of Precipitation

Science.gov (United States)

Penland, C.

2013-12-01

Both modified Poisson processes and compound Poisson processes can be relevant to stochastic parameterization of precipitation. This presentation compares the dynamical properties of these systems and discusses the physical situations in which each might be appropriate. If the parameters describing either class of systems originate in hydrodynamics, then proper consideration of stochastic calculus is required during numerical implementation of the parameterization. It is shown here that an improper numerical treatment can have severe implications for estimating rainfall distributions, particularly in the tails of the distributions and, thus, on the frequency of extreme events.

Stochastic quantization and gravity

International Nuclear Information System (INIS)

Rumpf, H.

1984-01-01

We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)

Consensus states of local majority rule in stochastic process

Energy Technology Data Exchange (ETDEWEB)

Luo, Yu-Pin [Department of Electronic Engineering, National Formosa University, Huwei, 63201, Taiwan (China); Tang, Chia-Wei; Xu, Hong-Yuan [Department of Physics, Chung-Yuan Christian University, Chungli, 32023, Taiwan (China); Wu, Jinn-Wen [Department of Applied Mathematics, Chung-Yuan Christian University, Chungli, 32023, Taiwan (China); Huang, Ming-Chang, E-mail: mchuang@cycu.edu.tw [Center for Theoretical Science and Department of Physics, Chung-Yuan Christian University, Chungli, 32023, Taiwan (China)

2015-04-03

A sufficient condition for a network system to reach a consensus state of the local majority rule is shown. The influence of interpersonal environment on the occurrence probability of consensus states for Watts–Strogatz and scale-free networks with random initial states is analyzed by numerical method. We also propose a stochastic local majority rule to study the mean first passage time from a random state to a consensus and the escape rate from a consensus state for systems in a noisy environment. Our numerical results show that there exists a window of fluctuation strengths for which the mean first passage time from a random to a consensus state reduces greatly, and the escape rate of consensus states obeys the Arrhenius equation in the window. - Highlights: • A sufficient condition for reaching a consensus. • The relation between the geometry of networks and the reachability of a consensus. • Stochastic local majority rule. • The mean first-passage time and the escape rate of consensus states.

Consensus states of local majority rule in stochastic process

International Nuclear Information System (INIS)

Luo, Yu-Pin; Tang, Chia-Wei; Xu, Hong-Yuan; Wu, Jinn-Wen; Huang, Ming-Chang

2015-01-01

A sufficient condition for a network system to reach a consensus state of the local majority rule is shown. The influence of interpersonal environment on the occurrence probability of consensus states for Watts–Strogatz and scale-free networks with random initial states is analyzed by numerical method. We also propose a stochastic local majority rule to study the mean first passage time from a random state to a consensus and the escape rate from a consensus state for systems in a noisy environment. Our numerical results show that there exists a window of fluctuation strengths for which the mean first passage time from a random to a consensus state reduces greatly, and the escape rate of consensus states obeys the Arrhenius equation in the window. - Highlights: • A sufficient condition for reaching a consensus. • The relation between the geometry of networks and the reachability of a consensus. • Stochastic local majority rule. • The mean first-passage time and the escape rate of consensus states

Stochastic models in reliability and maintenance

CERN Document Server

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...

Stochastic Models in the DORIS Position Time Series: Estimates from the IDS Contribution to the ITRF2014

Science.gov (United States)

Klos, A.; Bogusz, J.; Moreaux, G.

2017-12-01

This research focuses on the investigation of the deterministic and stochastic parts of the DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) weekly coordinate time series from the IDS contribution to the ITRF2014A set of 90 stations was divided into three groups depending on when the data was collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations (these three sum up to produce the Polynomial Trend Model) and a stochastic part, all being resolved with Maximum Likelihood Estimation (MLE). We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations, meaning that the most recent data are the most reliable ones. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. We examined five different noise models to be applied to the stochastic part of the DORIS time series: a pure white noise (WN), a pure power-law noise (PL), a combination of white and power-law noise (WNPL), an autoregressive process of first order (AR(1)) and a Generalized Gauss Markov model (GGM). From our study it arises that the PL process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from AR(1) to pure PL with few stations characterized by a positive spectral index.

Stochastic resonance driven by time-modulated correlated coloured noise sources in a single-mode laser

International Nuclear Information System (INIS)

De-Yi, Chen; Li, Zhang

2009-01-01

This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by time-modulated correlated coloured noise sources. The power spectrum and signal-to-noise ratio R of the laser intensity are calculated by the linear approximation. The effects caused by noise self-correlation time τ 1 , τ 2 and cross-correlated time τ 3 for stochastic resonance are analysed in two ways: τ 1 , τ 2 and τ 3 are taken to be the independent variables and the parameters respectively. The effects of the gain coefficient Γ and loss coefficient K on the stochastic resonance are also discussed. It is found that besides the presence of the standard form and the broad sense of stochastic resonance, the number of extrema in the curve of R versus K is reduced with the increase of the gain coefficient Γ

Bibliography on the stochastic processes in plasma and related problems

International Nuclear Information System (INIS)

Polovin, R.V.

1976-01-01

Stochastic processes in plasma and related matters. The bibliography contains 500 references and was compiled from the open literature only. Some references are annotated or completed with short abstracts. There are subject and authors indexes

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries.

Science.gov (United States)

Drawert, Brian; Engblom, Stefan; Hellander, Andreas

2012-06-22

Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at

Stochasticity in processes fundamentals and applications to chemistry and biology

CERN Document Server

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...

Aperiodic signals processing via parameter-tuning stochastic resonance in a photorefractive ring cavity

Directory of Open Access Journals (Sweden)

Xuefeng Li

2014-04-01

Full Text Available Based on solving numerically the generalized nonlinear Langevin equation describing the nonlinear dynamics of stochastic resonance by Fourth-order Runge-Kutta method, an aperiodic stochastic resonance based on an optical bistable system is numerically investigated. The numerical results show that a parameter-tuning stochastic resonance system can be realized by choosing the appropriate optical bistable parameters, which performs well in reconstructing aperiodic signals from a very high level of noise background. The influences of optical bistable parameters on the stochastic resonance effect are numerically analyzed via cross-correlation, and a maximum cross-correlation gain of 8 is obtained by optimizing optical bistable parameters. This provides a prospective method for reconstructing noise-hidden weak signals in all-optical signal processing systems.

Development of a generalized stochastic model for the analysis of monoenergetic space-time nuclear factor Kinetics

International Nuclear Information System (INIS)

Pham, Nhu Viet Ha

2011-02-01

To predict the space-time dependent behavior of a nuclear reactor, the conventional space-dependent kinetics equations are widely used for treating the spatial variables. However, the solutions of such deterministic space-dependent kinetics equations, which give only the mean values of the neutron population and the delayed neutron precursor concentrations, do not offer sufficient insight into the actual dynamic processes within a reactor, where the interacting populations vary randomly with space and time. It is also noted that at high power levels, the random behavior of a reactor is negligible but at low power levels, such as at start-up, random fluctuations in population dynamics can be significant. To mathematically describe the evolution of the state of a nuclear reactor using a set of stochastic kinetics equations, the forward stochastic model (FSM) in stochastic kinetics theory is devised through the concept of reactor transition probability and its probability generating function as the spatial domain of a reactor is partitioned into a number of space cells. Nevertheless, the FSM equations for the mean value of neutron and precursor distribution are deterministic-like. Furthermore, the numerical treatment of the FSM equations for the means, variances, and covariances is quite complicated and time-consuming. In the present study, a generalized stochastic model (called the stochastic space-dependent kinetics model or SSKM) based on the FSM and the Its stochastic differential equations was newly developed for the analysis of monoenergetic spacetime nuclear reactor kinetics in one dimension. First, the FSM equations for determining the mean values of neutron and delayed-neutron precursor populations were considered as the deterministic ones without taking into account their variances and covariances. Second, the system of interest was randomized again in the light of the Its stochastic differential equations in order to derive the SSKM. The proposed model

SDE decomposition and A-type stochastic interpretation in nonequilibrium processes

Science.gov (United States)

Yuan, Ruoshi; Tang, Ying; Ao, Ping

2017-12-01

An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochastic differential equation (SDE) into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the α-type interpretation for multidimensional systems. The potential landscape serves as a Hamiltonian-like function in nonequilibrium processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel framework. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.

A Constructive Sharp Approach to Functional Quantization of Stochastic Processes

OpenAIRE

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.

Automated Flight Routing Using Stochastic Dynamic Programming

Science.gov (United States)

Ng, Hok K.; Morando, Alex; Grabbe, Shon

2010-01-01

Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

Population density equations for stochastic processes with memory kernels

Science.gov (United States)

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.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

Science.gov (United States)

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.

Introduction to stochastic analysis integrals and differential equations

CERN Document Server

Mackevicius, Vigirdas

2013-01-01

This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion pro

Finite-size effects and switching times for Moran process with mutation.

Science.gov (United States)

DeVille, Lee; Galiardi, Meghan

2017-04-01

We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population. We also show that the stochastic system has asymmetries in the form of a skew for parameter values where the deterministic limit is symmetric.

Brownian motion, martingales, and stochastic calculus

CERN Document Server

Le Gall, Jean-François

2016-01-01

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

Stochastic evolution of the Universe: A possible dynamical process ...

Indian Academy of Sciences (India)

C Sivakumar

2017-12-11

Dec 11, 2017 ... https://doi.org/10.1007/s12043-017-1491-z. Stochastic evolution of the Universe: A possible dynamical process leading to fractal structures. C SIVAKUMAR. Department of Physics, Maharaja's College, Ernakulam 682 011, India. E-mail: thrisivc@yahoo.com. MS received 6 July 2016; revised 26 June 2017; ...

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

OpenAIRE

Xiao-Li Ding; Juan J. Nieto

2018-01-01

In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...

The stochastic versus the Euclidean approach to quantum fields on a static space-time

International Nuclear Information System (INIS)

De Angelis, G.F.; de Falco, D.

1986-01-01

Equations are presented which modify the definition of the Gaussian field in the Rindler chart in order to make contact with the Wightman state, the Hartle-Hawking state, and the Euclidean field. By taking Ornstein-Uhlenbeck processes the authors have chosen, in the sense of stochastic mechanics, to place precisely the Fulling modes in their harmonic oscillator ground state. In this respect, together with the periodicity of Minkowski space-time, the authors observe that the covariance of the Ornstein-Uhlenbeck process can be obtained by analytical continuation of the Wightman function of the harmonic oscillator at zero temperature

The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process

Science.gov (United States)

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 and long range dependence

CERN Document Server

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...

Universality in stochastic exponential growth.

Science.gov (United States)

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Exponential stability for stochastic delayed recurrent neural networks with mixed time-varying delays and impulses: the continuous-time case

International Nuclear Information System (INIS)

Karthik Raja, U; Leelamani, A; Raja, R; Samidurai, R

2013-01-01

In this paper, the exponential stability for a class of stochastic neural networks with time-varying delays and impulsive effects is considered. By constructing suitable Lyapunov functionals and by using the linear matrix inequality optimization approach, we obtain sufficient delay-dependent criteria to ensure the exponential stability of stochastic neural networks with time-varying delays and impulses. Two numerical examples with simulation results are provided to illustrate the effectiveness of the obtained results over those already existing in the literature. (paper)

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

Science.gov (United States)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Quantum learning of classical stochastic processes: The completely positive realization problem

International Nuclear Information System (INIS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

Quantum learning of classical stochastic processes: The completely positive realization problem

Science.gov (United States)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

Quantum learning of classical stochastic processes: The completely positive realization problem

Energy Technology Data Exchange (ETDEWEB)

Monràs, Alex [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Winter, Andreas [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); ICREA—Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys, 23, 08010 Barcelona (Spain)

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine

Analysis and Prediction on Vehicle Ownership Based on an Improved Stochastic Gompertz Diffusion Process

Directory of Open Access Journals (Sweden)

Huapu Lu

2017-01-01

Full Text Available This paper aims at introducing a new improved stochastic differential equation related to Gompertz curve for the projection of vehicle ownership growth. This diffusion model explains the relationship between vehicle ownership and GDP per capita, which has been studied as a Gompertz-like function before. The main innovations of the process lie in two parts: by modifying the deterministic part of the original Gompertz equation, the model can present the remaining slow increase when the S-shaped curve has reached its saturation level; by introducing the stochastic differential equation, the model can better fit the real data when there are fluctuations. Such comparisons are carried out based on data from US, UK, Japan, and Korea with a time span of 1960–2008. It turns out that the new process behaves better in fitting curves and predicting short term growth. Finally, a prediction of Chinese vehicle ownership up to 2025 is presented with the new model, as China is on the initial stage of motorization with much fluctuations in growth.

Stochastic goal-oriented error estimation with memory

Science.gov (United States)

Ackmann, Jan; Marotzke, Jochem; Korn, Peter

2017-11-01

We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.

12th Workshop on Stochastic Models, Statistics and Their Applications

CERN Document Server

Rafajłowicz, Ewaryst; Szajowski, Krzysztof

2015-01-01

This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.

Optimal Liquidation under Stochastic Liquidity

OpenAIRE

Becherer, Dirk; Bilarev, Todor; Frentrup, Peter

2016-01-01

We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determines the inter-temporal resilience of the market in spirit of Predoiu, Shaikhet and Shreve (2011), is taken to be stochastic, being driven by own random noise. The optimal contro...

Eco-reliable path finding in time-variant and stochastic networks

International Nuclear Information System (INIS)

Li, Wenjie; Yang, Lixing; Wang, Li; Zhou, Xuesong; Liu, Ronghui; Gao, Ziyou

2017-01-01

This paper addresses a route guidance problem for finding the most eco-reliable path in time-variant and stochastic networks such that travelers can arrive at the destination with the maximum on-time probability while meeting vehicle emission standards imposed by government regulators. To characterize the dynamics and randomness of transportation networks, the link travel times and emissions are assumed to be time-variant random variables correlated over the entire network. A 0–1 integer mathematical programming model is formulated to minimize the probability of late arrival by simultaneously considering the least expected emission constraint. Using the Lagrangian relaxation approach, the primal model is relaxed into a dualized model which is further decomposed into two simple sub-problems. A sub-gradient method is developed to reduce gaps between upper and lower bounds. Three sets of numerical experiments are tested to demonstrate the efficiency and performance of our proposed model and algorithm. - Highlights: • The most eco-reliable path is defined in time-variant and stochastic networks. • The model is developed with on-time arrival probability and emission constraints. • The sub-gradient and label correcting algorithm are integrated to solve the model. • Numerical experiments demonstrate the effectiveness of developed approaches.

Fault Detection for Non-Gaussian Stochastic Systems with Time-Varying Delay

Directory of Open Access Journals (Sweden)

Tao Li

2013-01-01

Full Text Available Fault detection (FD for non-Gaussian stochastic systems with time-varying delay is studied. The available information for the addressed problem is the input and the measured output probability density functions (PDFs of the system. In this framework, firstly, by constructing an augmented Lyapunov functional, which involves some slack variables and a tuning parameter, a delay-dependent condition for the existence of FD observer is derived in terms of linear matrix inequality (LMI and the fault can be detected through a threshold. Secondly, in order to improve the detection sensitivity performance, the optimal algorithm is applied to minimize the threshold value. Finally, paper-making process example is given to demonstrate the applicability of the proposed approach.

Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks

International Nuclear Information System (INIS)

Mathiyalagan, K.; Sakthivel, R.; Marshal Anthoni, S.

2012-01-01

This Letter addresses the stability analysis problem for a class of uncertain discrete-time stochastic fuzzy neural networks (DSFNNs) with time-varying delays. By constructing a new Lyapunov–Krasovskii functional combined with the free weighting matrix technique, a new set of delay-dependent sufficient conditions for the robust exponential stability of the considered DSFNNs is established in terms of Linear Matrix Inequalities (LMIs). Finally, numerical examples with simulation results are provided to illustrate the applicability and usefulness of the obtained theory. -- Highlights: ► Applications of neural networks require the knowledge of dynamic behaviors. ► Exponential stability of discrete-time stochastic fuzzy neural networks is studied. ► Linear matrix inequality optimization approach is used to obtain the result. ► Delay-dependent stability criterion is established in terms of LMIs. ► Examples with simulation are provided to show the effectiveness of the result.

Changing contributions of stochastic and deterministic processes in community assembly over a successional gradient.

Science.gov (United States)

Måren, Inger Elisabeth; Kapfer, Jutta; Aarrestad, Per Arild; Grytnes, John-Arvid; Vandvik, Vigdis

2018-01-01

Successional dynamics in plant community assembly may result from both deterministic and stochastic ecological processes. The relative importance of different ecological processes is expected to vary over the successional sequence, between different plant functional groups, and with the disturbance levels and land-use management regimes of the successional systems. We evaluate the relative importance of stochastic and deterministic processes in bryophyte and vascular plant community assembly after fire in grazed and ungrazed anthropogenic coastal heathlands in Northern Europe. A replicated series of post-fire successions (n = 12) were initiated under grazed and ungrazed conditions, and vegetation data were recorded in permanent plots over 13 years. We used redundancy analysis (RDA) to test for deterministic successional patterns in species composition repeated across the replicate successional series and analyses of co-occurrence to evaluate to what extent species respond synchronously along the successional gradient. Change in species co-occurrences over succession indicates stochastic successional dynamics at the species level (i.e., species equivalence), whereas constancy in co-occurrence indicates deterministic dynamics (successional niche differentiation). The RDA shows high and deterministic vascular plant community compositional change, especially early in succession. Co-occurrence analyses indicate stochastic species-level dynamics the first two years, which then give way to more deterministic replacements. Grazed and ungrazed successions are similar, but the early stage stochasticity is higher in ungrazed areas. Bryophyte communities in ungrazed successions resemble vascular plant communities. In contrast, bryophytes in grazed successions showed consistently high stochasticity and low determinism in both community composition and species co-occurrence. In conclusion, stochastic and individualistic species responses early in succession give way to more

Investment timing decisions in a stochastic duopoly model

Energy Technology Data Exchange (ETDEWEB)

Marseguerra, Giovanni [Istituto di Econometria e CRANEC, Universita Cattolica del Sacro Cuore di Milan (Italy)]. E-mail: giovanni.marseguerra@unicatt.it; Cortelezzi, Flavia [Dipartimento di Diritto ed Economia delle Persone e delle Imprese, Universita dell' Insubria (Italy)]. E-mail: flavia.cortelezzi@uninsubria.it; Dominioni, Armando [CORE-Catholique de Louvain la Neuve (Belgium)]. E-mail: dominioni@core.ucl.ac.be

2006-08-15

We investigate the role of strategic considerations on the optimal timing of investment when firms compete for a new market (e.g., the provision of an innovative product) under demand uncertainty. Within a continuous time model of stochastic oligopoly, we show that strategic considerations are likely to be of limited impact when the new product is radically innovative whilst the fear of a rival's entry may deeply affect firms' decisions whenever innovation is to some extent limited. The welfare analysis shows surprisingly that the desirability of the different market structures considered does not depend on the fixed entry cost.

Investment timing decisions in a stochastic duopoly model

International Nuclear Information System (INIS)

Marseguerra, Giovanni; Cortelezzi, Flavia; Dominioni, Armando

2006-01-01

We investigate the role of strategic considerations on the optimal timing of investment when firms compete for a new market (e.g., the provision of an innovative product) under demand uncertainty. Within a continuous time model of stochastic oligopoly, we show that strategic considerations are likely to be of limited impact when the new product is radically innovative whilst the fear of a rival's entry may deeply affect firms' decisions whenever innovation is to some extent limited. The welfare analysis shows surprisingly that the desirability of the different market structures considered does not depend on the fixed entry cost

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 measure theoretical approach to quantum stochastic processes

Energy Technology Data Exchange (ETDEWEB)

Waldenfels, Wilhelm von

2014-04-01

Authored by a leading researcher in the field. Self-contained presentation of the subject matter. Examines a number of worked examples in detail. 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.

Random migration processes between two stochastic epidemic centers.

Science.gov (United States)

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.

Bicriterion a priori route choice in stochastic time-dependent networks

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele

In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path...

Bicriterion a priori route choice in stochastic time-dependent networks

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Pretolani, D; Andersen, K A

2006-01-01

In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path...

Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass

Science.gov (United States)

Saleh, B. E. A.; Tavolacci, J. T.; Teich, M. C.

1981-01-01

Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.

Fixed-time synchronization of complex networks with nonidentical nodes and stochastic noise perturbations

Science.gov (United States)

Zhang, Wanli; Li, Chuandong; Huang, Tingwen; Huang, Junjian

2018-02-01

This paper investigates the fixed-time synchronization of complex networks (CNs) with nonidentical nodes and stochastic noise perturbations. By designing new controllers, constructing Lyapunov functions and using the properties of Weiner process, different synchronization criteria are derived according to whether the node systems in the CNs or the goal system satisfies the corresponding conditions. Moreover, the role of the designed controllers is analyzed in great detail by constructing a suitable comparison system and a new method is presented to estimate the settling time by utilizing the comparison system. Results of this paper can be applied to both directed and undirected weighted networks. Numerical simulations are offered to verify the effectiveness of our new results.

Stochastic Model Checking of the Stochastic Quality Calculus

DEFF Research Database (Denmark)

Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin

2015-01-01

The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input....... This gives rise to Generalised Semi-Markov Decision Processes for which few analytical techniques are available. We restrict delays on output actions to be exponentially distributed while still admitting real-time constraints on the quality binders. This facilitates developing analytical techniques based...

Stochastic estimation of electricity consumption

International Nuclear Information System (INIS)

Kapetanovic, I.; Konjic, T.; Zahirovic, Z.

1999-01-01

Electricity consumption forecasting represents a part of the stable functioning of the power system. It is very important because of rationality and increase of control process efficiency and development planning of all aspects of society. On a scientific basis, forecasting is a possible way to solve problems. Among different models that have been used in the area of forecasting, the stochastic aspect of forecasting as a part of quantitative models takes a very important place in applications. ARIMA models and Kalman filter as stochastic estimators have been treated together for electricity consumption forecasting. Therefore, the main aim of this paper is to present the stochastic forecasting aspect using short time series. (author)

Energy-Efficient FPGA-Based Parallel Quasi-Stochastic Computing

Directory of Open Access Journals (Sweden)

Ramu Seva

2017-11-01

Full Text Available The high performance of FPGA (Field Programmable Gate Array in image processing applications is justified by its flexible reconfigurability, its inherent parallel nature and the availability of a large amount of internal memories. Lately, the Stochastic Computing (SC paradigm has been found to be significantly advantageous in certain application domains including image processing because of its lower hardware complexity and power consumption. However, its viability is deemed to be limited due to its serial bitstream processing and excessive run-time requirement for convergence. To address these issues, a novel approach is proposed in this work where an energy-efficient implementation of SC is accomplished by introducing fast-converging Quasi-Stochastic Number Generators (QSNGs and parallel stochastic bitstream processing, which are well suited to leverage FPGA’s reconfigurability and abundant internal memory resources. The proposed approach has been tested on the Virtex-4 FPGA, and results have been compared with the serial and parallel implementations of conventional stochastic computation using the well-known SC edge detection and multiplication circuits. Results prove that by using this approach, execution time, as well as the power consumption are decreased by a factor of 3.5 and 4.5 for the edge detection circuit and multiplication circuit, respectively.

Distributed parallel computing in stochastic modeling of groundwater systems.

Science.gov (United States)

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.

Stochastic processes from physics to finance

CERN Document Server

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.

Histogram bin width selection for time-dependent Poisson processes

International Nuclear Information System (INIS)

Koyama, Shinsuke; Shinomoto, Shigeru

2004-01-01

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method

Histogram bin width selection for time-dependent Poisson processes

Energy Technology Data Exchange (ETDEWEB)

Koyama, Shinsuke; Shinomoto, Shigeru [Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502 (Japan)

2004-07-23

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.

Volatility Degree Forecasting of Stock Market by Stochastic Time Strength Neural Network

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Haiyan Mo

2013-01-01

Full Text Available In view of the applications of artificial neural networks in economic and financial forecasting, a stochastic time strength function is introduced in the backpropagation neural network model to predict the fluctuations of stock price changes. In this model, stochastic time strength function gives a weight for each historical datum and makes the model have the effect of random movement, and then we investigate and forecast the behavior of volatility degrees of returns for the Chinese stock market indexes and some global market indexes. The empirical research is performed in testing the prediction effect of SSE, SZSE, HSI, DJIA, IXIC, and S&P 500 with different selected volatility degrees in the established model.

Reconstructing the hidden states in time course data of stochastic models.

Science.gov (United States)

Zimmer, Christoph

2015-11-01

Parameter estimation is central for analyzing models in Systems Biology. The relevance of stochastic modeling in the field is increasing. Therefore, the need for tailored parameter estimation techniques is increasing as well. Challenges for parameter estimation are partial observability, measurement noise, and the computational complexity arising from the dimension of the parameter space. This article extends the multiple shooting for stochastic systems' method, developed for inference in intrinsic stochastic systems. The treatment of extrinsic noise and the estimation of the unobserved states is improved, by taking into account the correlation between unobserved and observed species. This article demonstrates the power of the method on different scenarios of a Lotka-Volterra model, including cases in which the prey population dies out or explodes, and a Calcium oscillation system. Besides showing how the new extension improves the accuracy of the parameter estimates, this article analyzes the accuracy of the state estimates. In contrast to previous approaches, the new approach is well able to estimate states and parameters for all the scenarios. As it does not need stochastic simulations, it is of the same order of speed as conventional least squares parameter estimation methods with respect to computational time. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Dimension reduction of Karhunen-Loeve expansion for simulation of stochastic processes

Science.gov (United States)

Liu, Zhangjun; Liu, Zixin; Peng, Yongbo

2017-11-01

Conventional Karhunen-Loeve expansions for simulation of stochastic processes often encounter the challenge of dealing with hundreds of random variables. For breaking through the barrier, a random function embedded Karhunen-Loeve expansion method is proposed in this paper. The updated scheme has a similar form to the conventional Karhunen-Loeve expansion, both involving a summation of a series of deterministic orthonormal basis and uncorrelated random variables. While the difference from the updated scheme lies in the dimension reduction of Karhunen-Loeve expansion through introducing random functions as a conditional constraint upon uncorrelated random variables. The random function is expressed as a single-elementary-random-variable orthogonal function in polynomial format (non-Gaussian variables) or trigonometric format (non-Gaussian and Gaussian variables). For illustrative purposes, the simulation of seismic ground motion is carried out using the updated scheme. Numerical investigations reveal that the Karhunen-Loeve expansion with random functions could gain desirable simulation results in case of a moderate sample number, except the Hermite polynomials and the Laguerre polynomials. It has the sound applicability and efficiency in simulation of stochastic processes. Besides, the updated scheme has the benefit of integrating with probability density evolution method, readily for the stochastic analysis of nonlinear structures.

A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution

Directory of Open Access Journals (Sweden)

Rice Sean H

2008-09-01

Full Text Available Abstract Background Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. Results I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Conclusion Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general

Stochastic analysis in discrete and continuous settings with normal martingales

CERN Document Server

Privault, Nicolas

2009-01-01

This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

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...

QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION

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A.E.Kobryn

2003-01-01

Full Text Available Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation. In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.

Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality

CERN Document Server

Saldi, Naci; Yüksel, Serdar

2018-01-01

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original mo...

On the adaptivity gap of stochastic orienteering

NARCIS (Netherlands)

Bansal, N.; Nagarajan, V.

2013-01-01

The input to the stochastic orienteering problem consists of a budget $B$ and metric $(V,d)$ where each vertex $v$ has a job with deterministic reward and random processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a

On the Adaptivity Gap of Stochastic Orienteering

NARCIS (Netherlands)

N. Bansal (Nikhil); V. Nagarajan

2013-01-01

htmlabstractThe input to the stochastic orienteering problem consists of a budget B and metric (V,d) where each vertex v has a job with deterministic reward and random processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a

Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors

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.

Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

Science.gov (United States)

Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

2017-12-01

The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Directory of Open Access Journals (Sweden)

Xiao-Li Ding

2018-01-01

Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

GCSRL - A Logic for Stochastic Reward Models with Timed and Untimed Behaviour

NARCIS (Netherlands)

Kuntz, Matthias; Haverkort, Boudewijn R.; Cloth, L.

In this paper we define the logic GCSRL (generalised continuous stochastic reward logic) that provides means to reason about systems that have states which sojourn times are either greater zero, in which case this sojourn time is exponentially distributed (tangible states), or zero (vanishing

Relevance of control theory to design and maintenance problems in time-variant reliability: The case of stochastic viability

International Nuclear Information System (INIS)

Rougé, Charles; Mathias, Jean-Denis; Deffuant, Guillaume

2014-01-01

The goal of this paper is twofold: (1) to show that time-variant reliability and a branch of control theory called stochastic viability address similar problems with different points of view, and (2) to demonstrate the relevance of concepts and methods from stochastic viability in reliability problems. On the one hand, reliability aims at evaluating the probability of failure of a system subjected to uncertainty and stochasticity. On the other hand, viability aims at maintaining a controlled dynamical system within a survival set. When the dynamical system is stochastic, this work shows that a viability problem belongs to a specific class of design and maintenance problems in time-variant reliability. Dynamic programming, which is used for solving Markovian stochastic viability problems, then yields the set of design states for which there exists a maintenance strategy which guarantees reliability with a confidence level β for a given period of time T. Besides, it leads to a straightforward computation of the date of the first outcrossing, informing on when the system is most likely to fail. We illustrate this approach with a simple example of population dynamics, including a case where load increases with time. - Highlights: • Time-variant reliability tools cannot devise complex maintenance strategies. • Stochastic viability is a control theory that computes a probability of failure. • Some design and maintenance problems are stochastic viability problems. • Used in viability, dynamic programming can find reliable maintenance actions. • Confronting reliability and control theories such as viability is promising

Main Achievements 2003-2004 - Interdisciplinary Research - Applications of theoretical physics - Stochastic processes

International Nuclear Information System (INIS)

2005-01-01

Some specific stochastic, jumping processes have been studied. They are defined in terms of the jump size distribution and the waiting time distribution which are mutually dependent. For the simplest case (the kangaroo process), the corresponding master equation has been completely solved and simple asymptotic expressions for the time-dependent probability distributions have been derived. A generalized version of that process, which takes into account the memory effects, has been proposed and a connection to transport processes, namely to the Boltzmann kinetic theory and diffusion, has been demonstrated. The same process, but defined on the circle instead of the axis, can possess the power law autocorrelation function; a simple formula for this function has been derived. Therefore, the process can serve as a useful model for the colored noises, in particular for the 1/f noise. It has been applied as a model of the driving force in the generalized Langevin equation, an impossible task with the standard kangaroo process. The equation has been solved by means of the Monte Carlo simulations. The resulting velocity and energy distributions exhibit extremely long memory about the initial conditions, despite an apparent fast equilibration of their comprehensive shape. The tails of both distributions fall faster than in the Maxwellian case

Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks

Science.gov (United States)

Forman, Yakir; Cameron, Maria

2017-07-01

We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size N onto stochastic networks, computing transition probabilities from the network for an N-particle cluster to the one for N+1, and connecting these networks into a single joint network. The attachment rate is a control parameter. The resulting network representing the aggregation of up to 14 particles contains 6427 vertices. It is not only time-irreversible but also reducible. To analyze its transient dynamics, we introduce the sequence of the expected initial and pre-attachment distributions and compute them for a wide range of attachment rates and three values of temperature. As a result, we find the configurations most likely to be observed in the process of aggregation for each cluster size. We examine the attachment process and conduct a structural analysis of the sets of local energy minima for every cluster size. We show that both processes taking place in the network, attachment and relaxation, lead to the dominance of icosahedral packing in small (up to 14 atom) clusters.

Robust stability for stochastic bidirectional associative memory neural networks with time delays

Science.gov (United States)

Shu, H. S.; Lv, Z. W.; Wei, G. L.

2008-02-01

In this paper, the asymptotic stability is considered for a class of uncertain stochastic bidirectional associative memory neural networks with time delays and parameter uncertainties. The delays are time-invariant and the uncertainties are norm-bounded that enter into all network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov-Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed criteria.

A study on the stochastic model for nuclide transport in the fractured porous rock using continuous time Markov process

International Nuclear Information System (INIS)

Lee, Youn Myoung

1995-02-01

As a newly approaching model, a stochastic model using continuous time Markov process for nuclide decay chain transport of arbitrary length in the fractured porous rock medium has been proposed, by which the need for solving a set of partial differential equations corresponding to various sets of side conditions can be avoided. Once the single planar fracture in the rock matrix is represented by a series of finite number of compartments having region wise constant parameter values in them, the medium is continuous in view of various processes associated with nuclide transport but discrete in medium space and such geologic system is assumed to have Markov property, since the Markov process requires that only the present value of the time dependent random variable be known to determine the future value of random variable, nuclide transport in the medium can then be modeled as a continuous time Markov process. Processes that are involved in nuclide transport are advective transport due to groundwater flow, diffusion into the rock matrix, adsorption onto the wall of the fracture and within the pores in the rock matrix, and radioactive decay chain. The transition probabilities for nuclide from the transition intensities between and out of the compartments are represented utilizing Chapman-Kolmogorov equation, through which the expectation and the variance of nuclide distribution for each compartment or the fractured rock medium can be obtained. Some comparisons between Markov process model developed in this work and available analytical solutions for one-dimensional layered porous medium, fractured medium with rock matrix diffusion, and porous medium considering three member nuclide decay chain without rock matrix diffusion have been made showing comparatively good agreement for all cases. To verify the model developed in this work another comparative study was also made by fitting the experimental data obtained with NaLS and uranine running in the artificial fractured

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process.

Science.gov (United States)

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2017-11-23

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.

On the small time asymptotics of 3D stochastic primitive equations

OpenAIRE

Dong, Zhao; Zhang, Rangrang

2017-01-01

In this paper, we establish a small time large deviation principle for the strong solution of 3D stochastic primitive equations driven by multiplicative noise. Both the small noise and the small, but highly nonlinear, unbounded nonlinear terms should be taken into consideration.

Assessing and accounting for time heterogeneity in stochastic actor oriented models

NARCIS (Netherlands)

Lospinoso, Joshua A.; Schweinberger, Michael; Snijders, Tom A. B.; Ripley, Ruth M.

This paper explores time heterogeneity in stochastic actor oriented models (SAOM) proposed by Snijders (Sociological methodology. Blackwell, Boston, pp 361-395, 2001) which are meant to study the evolution of networks. SAOMs model social networks as directed graphs with nodes representing people,

Urban Freight Management with Stochastic Time-Dependent Travel Times and Application to Large-Scale Transportation Networks

Directory of Open Access Journals (Sweden)

Shichao Sun

2015-01-01

Full Text Available This paper addressed the vehicle routing problem (VRP in large-scale urban transportation networks with stochastic time-dependent (STD travel times. The subproblem which is how to find the optimal path connecting any pair of customer nodes in a STD network was solved through a robust approach without requiring the probability distributions of link travel times. Based on that, the proposed STD-VRP model can be converted into solving a normal time-dependent VRP (TD-VRP, and algorithms for such TD-VRPs can also be introduced to obtain the solution. Numerical experiments were conducted to address STD-VRPTW of practical sizes on a real world urban network, demonstrated here on the road network of Shenzhen, China. The stochastic time-dependent link travel times of the network were calibrated by historical floating car data. A route construction algorithm was applied to solve the STD problem in 4 delivery scenarios efficiently. The computational results showed that the proposed STD-VRPTW model can improve the level of customer service by satisfying the time-window constraint under any circumstances. The improvement can be very significant especially for large-scale network delivery tasks with no more increase in cost and environmental impacts.

Stochastic Calculus and Differential Equations for Physics and Finance

Science.gov (United States)

McCauley, Joseph L.

2013-02-01

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

Disentangling mechanisms that mediate the balance between stochastic and deterministic processes in microbial succession.

Science.gov (United States)

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.

Modified stochastic fragmentation of an interval as an ageing process

Science.gov (United States)

Fortin, Jean-Yves

2018-02-01

We study a stochastic model based on modified fragmentation of a finite interval. The mechanism consists of cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve the interval length. This leads to a set of segments of random sizes, with the accumulation of small fragments near the origin. This model is an example of record dynamics, with the presence of ‘quakes’ and slow dynamics. The fragment size distribution is a universal inverse power law with logarithmic corrections. The exact distribution for the fragment number as function of time is simply related to the unsigned Stirling numbers of the first kind. Two-time correlation functions are defined, and computed exactly. They satisfy scaling relations, and exhibit aging phenomena. In particular, the probability that the same number of fragments is found at two different times t>s is asymptotically equal to [4πlog(s)]-1/2 when s\\gg 1 and the ratio t/s is fixed, in agreement with the numerical simulations. The same process with a reset impedes the aging phenomenon-beyond a typical time scale defined by the reset parameter.

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.

Synchronization of a Class of Memristive Stochastic Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays via Sampled-Data Control

Directory of Open Access Journals (Sweden)

Manman Yuan

2018-01-01

Full Text Available The paper addresses the issue of synchronization of memristive bidirectional associative memory neural networks (MBAMNNs with mixed time-varying delays and stochastic perturbation via a sampled-data controller. First, we propose a new model of MBAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying distributed delays and discrete delays. Second, we design a new method of sampled-data control for the stochastic MBAMNNs. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the methods are carefully designed to confirm the synchronization processes are suitable for the feather of the memristor. Third, sufficient criteria guaranteeing the synchronization of the systems are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

Stochastic modeling of stock price process induced from the conjugate heat equation

Science.gov (United States)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

On the adaptivity gap of stochastic orienteering

NARCIS (Netherlands)

Bansal, N.; Nagarajan, V.; Lee, J.; Vygen, J.

2014-01-01

The input to the stochastic orienteering problem [14] consists of a budget B and metric (V,d) where each vertex v¿¿¿V has a job with a deterministic reward and a random processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a

On the adaptivity gap of stochastic orienteering

NARCIS (Netherlands)

Bansal, N.; Nagarajan, V.

2015-01-01

The input to the stochastic orienteering problem (Gupta et al. in SODA, pp 1522–1538,  2012) consists of a budget B and metric (V, d) where each vertex(Formula presented.) has a job with a deterministic reward and a random processing time (drawn from a known distribution). The processing times are

Stochastic models in the DORIS position time series: estimates for IDS contribution to ITRF2014

Science.gov (United States)

Klos, Anna; Bogusz, Janusz; Moreaux, Guilhem

2017-11-01

This paper focuses on the investigation of the deterministic and stochastic parts of the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) weekly time series aligned to the newest release of ITRF2014. A set of 90 stations was divided into three groups depending on when the data were collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations and a stochastic part, all being estimated with maximum likelihood estimation. We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations. The quality of the most recent data has significantly improved. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. Among several tested models, the power-law process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from an autoregressive process to pure power-law noise with few stations characterised by a positive spectral index. For the latest observations, the medians of the velocity errors were equal to 0.3, 0.3 and 0.4 mm/year, respectively, for the North, East and Up components. In the best cases, a velocity uncertainty of DORIS sites of 0.1 mm/year is achievable when the appropriate coloured noise model is taken into consideration.

A General Theory of Markovian Time Inconsistent Stochastic Control Problems

DEFF Research Database (Denmark)

Björk, Tomas; Murgochi, Agatha

We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...

Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations

Science.gov (United States)

Krylov, N. V.; Priola, E.

2017-09-01

We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.

Multistage stochastic optimization

CERN Document Server

Pflug, Georg Ch

2014-01-01

Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization.  It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book

Scheduling stochastic two-machine flow shop problems to minimize expected makespan

Directory of Open Access Journals (Sweden)

Mehdi Heydari

2013-07-01

Full Text Available During the past few years, despite tremendous contribution on deterministic flow shop problem, there are only limited number of works dedicated on stochastic cases. This paper examines stochastic scheduling problems in two-machine flow shop environment for expected makespan minimization where processing times of jobs are normally distributed. Since jobs have stochastic processing times, to minimize the expected makespan, the expected sum of the second machine’s free times is minimized. In other words, by minimization waiting times for the second machine, it is possible to reach the minimum of the objective function. A mathematical method is proposed which utilizes the properties of the normal distributions. Furthermore, this method can be used as a heuristic method for other distributions, as long as the means and variances are available. The performance of the proposed method is explored using some numerical examples.

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

Science.gov (United States)

Liu, Zhangjun; Liu, Zenghui; Peng, Yongbo

2018-03-01

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.

Designing time-of-use program based on stochastic security constrained unit commitment considering reliability index

International Nuclear Information System (INIS)

Nikzad, Mehdi; Mozafari, Babak; Bashirvand, Mahdi; Solaymani, Soodabeh; Ranjbar, Ali Mohamad

2012-01-01

Recently in electricity markets, a massive focus has been made on setting up opportunities for participating demand side. Such opportunities, also known as demand response (DR) options, are triggered by either a grid reliability problem or high electricity prices. Two important challenges that market operators are facing are appropriate designing and reasonable pricing of DR options. In this paper, time-of-use program (TOU) as a prevalent time-varying program is modeled linearly based on own and cross elasticity definition. In order to decide on TOU rates, a stochastic model is proposed in which the optimum TOU rates are determined based on grid reliability index set by the operator. Expected Load Not Supplied (ELNS) is used to evaluate reliability of the power system in each hour. The proposed stochastic model is formulated as a two-stage stochastic mixed-integer linear programming (SMILP) problem and solved using CPLEX solver. The validity of the method is tested over the IEEE 24-bus test system. In this regard, the impact of the proposed pricing method on system load profile; operational costs and required capacity of up- and down-spinning reserve as well as improvement of load factor is demonstrated. Also the sensitivity of the results to elasticity coefficients is investigated. -- Highlights: ► Time-of-use demand response program is linearly modeled. ► A stochastic model is proposed to determine the optimum TOU rates based on ELNS index set by the operator. ► The model is formulated as a short-term two-stage stochastic mixed-integer linear programming problem.

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

Effects of demographic stochasticity on biological community assembly on evolutionary time scales

KAUST Repository

Murase, Yohsuke; Shimada, Takashi; Ito, Nobuyasu; Rikvold, Per Arne

2010-01-01

We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.

Effects of demographic stochasticity on biological community assembly on evolutionary time scales

KAUST Repository

Murase, Yohsuke

2010-04-13

We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.

Monte Carlo simulation of induction time and metastable zone width; stochastic or deterministic?

Science.gov (United States)

Kubota, Noriaki

2018-03-01

The induction time and metastable zone width (MSZW) measured for small samples (say 1 mL or less) both scatter widely. Thus, these two are observed as stochastic quantities. Whereas, for large samples (say 1000 mL or more), the induction time and MSZW are observed as deterministic quantities. The reason for such experimental differences is investigated with Monte Carlo simulation. In the simulation, the time (under isothermal condition) and supercooling (under polythermal condition) at which a first single crystal is detected are defined as the induction time t and the MSZW ΔT for small samples, respectively. The number of crystals just at the moment of t and ΔT is unity. A first crystal emerges at random due to the intrinsic nature of nucleation, accordingly t and ΔT become stochastic. For large samples, the time and supercooling at which the number density of crystals N/V reaches a detector sensitivity (N/V)det are defined as t and ΔT for isothermal and polythermal conditions, respectively. The points of t and ΔT are those of which a large number of crystals have accumulated. Consequently, t and ΔT become deterministic according to the law of large numbers. Whether t and ΔT may stochastic or deterministic in actual experiments should not be attributed to change in nucleation mechanisms in molecular level. It could be just a problem caused by differences in the experimental definition of t and ΔT.

Stochastic Evolution Dynamic of the Rock-Scissors-Paper Game Based on a Quasi Birth and Death Process.

Science.gov (United States)

Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu

2016-06-27

Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

Aboveground and belowground arthropods experience different relative influences of stochastic versus deterministic community assembly processes following disturbance

Directory of Open Access Journals (Sweden)

Scott Ferrenberg

2016-10-01

Full Text Available Background Understanding patterns of biodiversity is a longstanding challenge in ecology. Similar to other biotic groups, arthropod community structure can be shaped by deterministic and stochastic processes, with limited understanding of what moderates the relative influence of these processes. Disturbances have been noted to alter the relative influence of deterministic and stochastic processes on community assembly in various study systems, implicating ecological disturbances as a potential moderator of these forces. Methods Using a disturbance gradient along a 5-year chronosequence of insect-induced tree mortality in a subalpine forest of the southern Rocky Mountains, Colorado, USA, we examined changes in community structure and relative influences of deterministic and stochastic processes in the assembly of aboveground (surface and litter-active species and belowground (species active in organic and mineral soil layers arthropod communities. Arthropods were sampled for all years of the chronosequence via pitfall traps (aboveground community and modified Winkler funnels (belowground community and sorted to morphospecies. Community structure of both communities were assessed via comparisons of morphospecies abundance, diversity, and composition. Assembly processes were inferred from a mixture of linear models and matrix correlations testing for community associations with environmental properties, and from null-deviation models comparing observed vs. expected levels of species turnover (Beta diversity among samples. Results Tree mortality altered community structure in both aboveground and belowground arthropod communities, but null models suggested that aboveground communities experienced greater relative influences of deterministic processes, while the relative influence of stochastic processes increased for belowground communities. Additionally, Mantel tests and linear regression models revealed significant associations between the

Aboveground and belowground arthropods experience different relative influences of stochastic versus deterministic community assembly processes following disturbance

Science.gov (United States)

Martinez, Alexander S.; Faist, Akasha M.

2016-01-01

Background Understanding patterns of biodiversity is a longstanding challenge in ecology. Similar to other biotic groups, arthropod community structure can be shaped by deterministic and stochastic processes, with limited understanding of what moderates the relative influence of these processes. Disturbances have been noted to alter the relative influence of deterministic and stochastic processes on community assembly in various study systems, implicating ecological disturbances as a potential moderator of these forces. Methods Using a disturbance gradient along a 5-year chronosequence of insect-induced tree mortality in a subalpine forest of the southern Rocky Mountains, Colorado, USA, we examined changes in community structure and relative influences of deterministic and stochastic processes in the assembly of aboveground (surface and litter-active species) and belowground (species active in organic and mineral soil layers) arthropod communities. Arthropods were sampled for all years of the chronosequence via pitfall traps (aboveground community) and modified Winkler funnels (belowground community) and sorted to morphospecies. Community structure of both communities were assessed via comparisons of morphospecies abundance, diversity, and composition. Assembly processes were inferred from a mixture of linear models and matrix correlations testing for community associations with environmental properties, and from null-deviation models comparing observed vs. expected levels of species turnover (Beta diversity) among samples. Results Tree mortality altered community structure in both aboveground and belowground arthropod communities, but null models suggested that aboveground communities experienced greater relative influences of deterministic processes, while the relative influence of stochastic processes increased for belowground communities. Additionally, Mantel tests and linear regression models revealed significant associations between the aboveground arthropod

Quantitative sociodynamics stochastic methods and models of social interaction processes

CERN Document Server

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

CERN Document Server

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...

Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps

OpenAIRE

Li, Yan; Hu, Junhao

2013-01-01

We investigate the convergence rate of Euler-Maruyama method for a class of stochastic partial differential delay equations driven by both Brownian motion and Poisson point processes. We discretize in space by a Galerkin method and in time by using a stochastic exponential integrator. We generalize some results of Bao et al. (2011) and Jacob et al. (2009) in finite dimensions to a class of stochastic partial differential delay equations with jumps in infinite dimensions.

Stochastic Simulation and Forecast of Hydrologic Time Series Based on Probabilistic Chaos Expansion

Science.gov (United States)

Li, Z.; Ghaith, M.

2017-12-01

Hydrological processes are characterized by many complex features, such as nonlinearity, dynamics and uncertainty. How to quantify and address such complexities and uncertainties has been a challenging task for water engineers and managers for decades. To support robust uncertainty analysis, an innovative approach for the stochastic simulation and forecast of hydrologic time series is developed is this study. Probabilistic Chaos Expansions (PCEs) are established through probabilistic collocation to tackle uncertainties associated with the parameters of traditional hydrological models. The uncertainties are quantified in model outputs as Hermite polynomials with regard to standard normal random variables. Sequentially, multivariate analysis techniques are used to analyze the complex nonlinear relationships between meteorological inputs (e.g., temperature, precipitation, evapotranspiration, etc.) and the coefficients of the Hermite polynomials. With the established relationships between model inputs and PCE coefficients, forecasts of hydrologic time series can be generated and the uncertainties in the future time series can be further tackled. The proposed approach is demonstrated using a case study in China and is compared to a traditional stochastic simulation technique, the Markov-Chain Monte-Carlo (MCMC) method. Results show that the proposed approach can serve as a reliable proxy to complicated hydrological models. It can provide probabilistic forecasting in a more computationally efficient manner, compared to the traditional MCMC method. This work provides technical support for addressing uncertainties associated with hydrological modeling and for enhancing the reliability of hydrological modeling results. Applications of the developed approach can be extended to many other complicated geophysical and environmental modeling systems to support the associated uncertainty quantification and risk analysis.

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

Science.gov (United States)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks.

Science.gov (United States)

Vestergaard, Christian L; Génois, Mathieu

2015-10-01

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.

Front Propagation in Stochastic Neural Fields

KAUST Repository

Bressloff, Paul C.

2012-01-01

We analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein-Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive. © 2012 Society for Industrial and Applied Mathematics.

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

Energy Technology Data Exchange (ETDEWEB)

Hosking, John Joseph Absalom, E-mail: j.j.a.hosking@cma.uio.no [University of Oslo, Centre of Mathematics for Applications (CMA) (Norway)

2012-12-15

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

International Nuclear Information System (INIS)

Hosking, John Joseph Absalom

2012-01-01

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966–979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197–216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

Stochastic Pi-calculus Revisited

DEFF Research Database (Denmark)

Cardelli, Luca; Mardare, Radu Iulian

2013-01-01

We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...

Applied probability and stochastic processes. 2. ed.

Energy Technology Data Exchange (ETDEWEB)

Feldman, Richard M. [Texas A and M Univ., College Station, TX (United States). Industrial and Systems Engineering Dept.; Valdez-Flores, Ciriaco [Sielken and Associates Consulting, Inc., Bryan, TX (United States)

2010-07-01

This book presents applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications of the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. The initial chapters present a summary of probability and statistics and then Poisson processes, Markov chains, Markov processes and queuing processes are introduced. Advanced topics include simulation, inventory theory, replacement theory, Markov decision theory, and the use of matrix geometric procedures in the analysis of queues. Included in the second edition are appendices at the end of several chapters giving suggestions for the use of Excel in solving the problems of the chapter. Also new in this edition are an introductory chapter on statistics and a chapter on Poisson processes that includes some techniques used in risk assessment. The old chapter on queues has been expanded and broken into two new chapters: one for simple queuing processes and one for queuing networks. Support is provided through the web site http://apsp.tamu.edu where students will have the answers to odd numbered problems and instructors will have access to full solutions and Excel files for homework. (orig.)

Early detection of metabolic and energy disorders by thermal time series stochastic complexity analysis

Energy Technology Data Exchange (ETDEWEB)

Lutaif, N.A. [Departamento de Clínica Médica, Faculdade de Ciências Médicas, Universidade Estadual de Campinas, Campinas, SP (Brazil); Palazzo, R. Jr [Departamento de Telemática, Faculdade de Engenharia Elétrica e Computação, Universidade Estadual de Campinas, Campinas, SP (Brazil); Gontijo, J.A.R. [Departamento de Clínica Médica, Faculdade de Ciências Médicas, Universidade Estadual de Campinas, Campinas, SP (Brazil)

2014-01-17

Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile.

Early detection of metabolic and energy disorders by thermal time series stochastic complexity analysis

International Nuclear Information System (INIS)

Lutaif, N.A.; Palazzo, R. Jr; Gontijo, J.A.R.

2014-01-01

Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile

A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

Directory of Open Access Journals (Sweden)

Elisa Alòs

2008-01-01

Full Text Available We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

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.

Disentangling mechanisms that mediate the balance between stochastic and deterministic processes in microbial succession

NARCIS (Netherlands)

Dini-Andreote, Francisco; Stegen, James C.; van Elsas, Jan Dirk; Salles, Joana Falcao

2015-01-01

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

A Simulation-Based Dynamic Stochastic Route Choice Model for Evacuation

Directory of Open Access Journals (Sweden)

Xing Zhao

2012-01-01

Full Text Available This paper establishes a dynamic stochastic route choice model for evacuation to simulate the propagation process of traffic flow and estimate the stochastic route choice under evacuation situations. The model contains a lane-group-based cell transmission model (CTM which sets different traffic capacities for links with different turning movements to flow out in an evacuation situation, an actual impedance model which is to obtain the impedance of each route in time units at each time interval and a stochastic route choice model according to the probit-based stochastic user equilibrium. In this model, vehicles loading at each origin at each time interval are assumed to choose an evacuation route under determinate road network, signal design, and OD demand. As a case study, the proposed model is validated on the network nearby Nanjing Olympic Center after the opening ceremony of the 10th National Games of the People's Republic of China. The traffic volumes and clearing time at five exit points of the evacuation zone are calculated by the model to compare with survey data. The results show that this model can appropriately simulate the dynamic route choice and evolution process of the traffic flow on the network in an evacuation situation.

Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation

DEFF Research Database (Denmark)

Tahavori, Maryamsadat; Shaker, Hamid Reza

2012-01-01

A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...... by using the concept and properties of the reciprocal systems. The results are further illustrated by two practical numerical examples: a model of CD player and a model of the atmospheric storm track....

Soil Erosion as a stochastic process

Science.gov (United States)

Casper, Markus C.

2015-04-01

corrected experimentally. To overcome this disadvantage of our actual models, soil erosion models are needed that are able to use stochastic directly variables and parameter distributions. There are only some minor approaches in this direction. The most advanced is the model "STOSEM" proposed by Sidorchuk in 2005. In this model, only a small part of the soil erosion processes is described, the aggregate detachment and the aggregate transport by flowing water. The concept is highly simplified, for example, many parameters are temporally invariant. Nevertheless, the main problem is that our existing measurements and experiments are not geared to provide stochastic parameters (e.g. as probability density functions); in the best case they deliver a statistical validation of the mean values. Again, we get effective parameters, spatially and temporally averaged. There is an urgent need for laboratory and field experiments on overland flow structure, raindrop effects and erosion rate, which deliver information on spatial and temporal structure of soil and surface properties and processes.

Statistical inference for discrete-time samples from affine stochastic delay differential equations

DEFF Research Database (Denmark)

Küchler, Uwe; Sørensen, Michael

2013-01-01

Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class of prediction-based estimating functions is investigated...

Stochastic Thermodynamics: A Dynamical Systems Approach

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Tanmay Rajpurohit

2017-12-01

Full Text Available In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time.

Simulation of Stochastic Processes by Coupled ODE-PDE

Science.gov (United States)

Zak, Michail

2008-01-01

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut

Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on genera...

Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.

Directory of Open Access Journals (Sweden)

Giorgos Minas

2017-07-01

Full Text Available In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA overcomes the main limitations of the standard Linear Noise Approximation (LNA to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.

Global synchronization of general delayed complex networks with stochastic disturbances

International Nuclear Information System (INIS)

Tu Li-Lan

2011-01-01

In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito's differential rule and the linear matrix inequality (LMI) optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions. (general)

Asymptotic analysis for functional stochastic differential equations

CERN Document Server

Bao, Jianhai; Yuan, Chenggui

2016-01-01

This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity. This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.

Jumps and stochastic volatility in oil prices: Time series evidence

International Nuclear Information System (INIS)

Larsson, Karl; Nossman, Marcus

2011-01-01

In this paper we examine the empirical performance of affine jump diffusion models with stochastic volatility in a time series study of crude oil prices. We compare four different models and estimate them using the Markov Chain Monte Carlo method. The support for a stochastic volatility model including jumps in both prices and volatility is strong and the model clearly outperforms the others in terms of a superior fit to data. Our estimation method allows us to obtain a detailed study of oil prices during two periods of extreme market stress included in our sample; the Gulf war and the recent financial crisis. We also address the economic significance of model choice in two option pricing applications. The implied volatilities generated by the different estimated models are compared and we price a real option to develop an oil field. Our findings indicate that model choice can have a material effect on the option values.

Power Laws in Stochastic Processes for Social Phenomena: An Introductory Review

Science.gov (United States)

Kumamoto, Shin-Ichiro; Kamihigashi, Takashi

2018-03-01

Many phenomena with power laws have been observed in various fields of the natural and social sciences, and these power laws are often interpreted as the macro behaviors of systems that consist of micro units. In this paper, we review some basic mathematical mechanisms that are known to generate power laws. In particular, we focus on stochastic processes including the Yule process and the Simon process as well as some recent models. The main purpose of this paper is to explain the mathematical details of their mechanisms in a self-contained manner.

TIME-DEPENDENT STOCHASTIC ACCELERATION MODEL FOR FERMI BUBBLES

Energy Technology Data Exchange (ETDEWEB)

Sasaki, Kento; Asano, Katsuaki; Terasawa, Toshio, E-mail: kentos@icrr.u-tokyo.ac.jp, E-mail: asanok@icrr.u-tokyo.ac.jp, E-mail: terasawa@icrr.u-tokyo.ac.jp [Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582 (Japan)

2015-12-01

We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin–Helmholtz, Rayleigh–Taylor, or Richtmyer–Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is different from those for a steady solution. We also show that the contribution of electrons that escaped from the acceleration regions significantly softens the photon spectrum. The photon spectrum and surface brightness profile are reproduced by our models. If the escape efficiency is very high, the radio flux from the escaped low-energy electrons can be comparable to that of the WMAP haze. We also demonstrate hadronic models with the stochastic acceleration, but they are unlikely in the viewpoint of the energy budget.

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

Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

2016-07-01

The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

Multimodal Network Equilibrium with Stochastic Travel Times

Directory of Open Access Journals (Sweden)

M. Meng

2014-01-01

Full Text Available The private car, unlike public traffic modes (e.g., subway, trolley running along dedicated track-ways, is invariably subject to various uncertainties resulting in travel time variation. A multimodal network equilibrium model is formulated that explicitly considers stochastic link capacity variability in the road network. The travel time of combined-mode trips is accumulated based on the concept of the mean excess travel time (METT which is a summation of estimated buffer time and tardy time. The problem is characterized by an equivalent VI (variational inequality formulation where the mode choice is expressed in a hierarchical logit structure. Specifically, the supernetwork theory and expansion technique are used herein to represent the multimodal transportation network, which completely represents the combined-mode trips as constituting multiple modes within a trip. The method of successive weighted average is adopted for problem solutions. The model and solution method are further applied to study the trip distribution and METT variations caused by the different levels of the road conditions. Results of numerical examples show that travelers prefer to choose the combined travel mode as road capacity decreases. Travelers with different attitudes towards risk are shown to exhibit significant differences when making travel choice decisions.

A stochastic programming approach to manufacturing flow control

OpenAIRE

Haurie, Alain; Moresino, Francesco

2012-01-01

This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochastic programming approach on a suitably discretized and sampled system. The method proceeds through two stages: (i) the Hamilton-Jacobi-Bellman (HJB) dynamic programming equations for the finite horizon continuous time stochastic control problem are discretized over a set of sample...