Space-time-modulated stochastic processes
Giona, Massimiliano
2017-10-01
Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.
Computer Aided Continuous Time Stochastic Process Modelling
DEFF Research Database (Denmark)
Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay
2001-01-01
A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...
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)
Borodin, Andrei N
2017-01-01
This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Parzen, Emanuel
1962-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
Time-variant reliability assessment through equivalent stochastic process transformation
International Nuclear Information System (INIS)
Wang, Zequn; Chen, Wei
2016-01-01
Time-variant reliability measures the probability that an engineering system successfully performs intended functions over a certain period of time under various sources of uncertainty. In practice, it is computationally prohibitive to propagate uncertainty in time-variant reliability assessment based on expensive or complex numerical models. This paper presents an equivalent stochastic process transformation approach for cost-effective prediction of reliability deterioration over the life cycle of an engineering system. To reduce the high dimensionality, a time-independent reliability model is developed by translating random processes and time parameters into random parameters in order to equivalently cover all potential failures that may occur during the time interval of interest. With the time-independent reliability model, an instantaneous failure surface is attained by using a Kriging-based surrogate model to identify all potential failure events. To enhance the efficacy of failure surface identification, a maximum confidence enhancement method is utilized to update the Kriging model sequentially. Then, the time-variant reliability is approximated using Monte Carlo simulations of the Kriging model where system failures over a time interval are predicted by the instantaneous failure surface. The results of two case studies demonstrate that the proposed approach is able to accurately predict the time evolution of system reliability while requiring much less computational efforts compared with the existing analytical approach. - Highlights: • Developed a new approach for time-variant reliability analysis. • Proposed a novel stochastic process transformation procedure to reduce the dimensionality. • Employed Kriging models with confidence-based adaptive sampling scheme to enhance computational efficiency. • The approach is effective for handling random process in time-variant reliability analysis. • Two case studies are used to demonstrate the efficacy
Time Series, Stochastic Processes and Completeness of Quantum Theory
International Nuclear Information System (INIS)
Kupczynski, Marian
2011-01-01
Most of physical experiments are usually described as repeated measurements of some random variables. Experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared with the probabilities provided by the algorithms of quantum theory (QT). In spite of statistical predictions of QT a claim was made that it provided the most complete description of the data and of the underlying physical phenomena. This claim could be easily rejected if some fine structures, averaged out in the standard descriptive statistical analysis, were found in time series of experimental data. To search for these structures one has to use more subtle statistical tools which were developed to study time series produced by various stochastic processes. In this talk we review some of these tools. As an example we show how the standard descriptive statistical analysis of the data is unable to reveal a fine structure in a simulated sample of AR (2) stochastic process. We emphasize once again that the violation of Bell inequalities gives no information on the completeness or the non locality of QT. The appropriate way to test the completeness of quantum theory is to search for fine structures in time series of the experimental data by means of the purity tests or by studying the autocorrelation and partial autocorrelation functions.
Susceptibility of optimal train schedules to stochastic disturbances of process times
DEFF Research Database (Denmark)
Larsen, Rune; Pranzo, Marco; D’Ariano, Andrea
2013-01-01
study, an advanced branch and bound algorithm, on average, outperforms a First In First Out scheduling rule both in deterministic and stochastic traffic scenarios. However, the characteristic of the stochastic processes and the way a stochastic instance is handled turn out to have a serious impact...... and dwell times). In fact, the objective of railway traffic management is to reduce delay propagation and to increase disturbance robustness of train schedules at a network scale. We present a quantitative study of traffic disturbances and their effects on the schedules computed by simple and advanced...
Doubly stochastic Poisson process models for precipitation at fine time-scales
Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao
2012-09-01
This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
Capasso, Vincenzo
2015-01-01
This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics, and epidemics * Agent-based models New to the Third Edition: * Infinitely divisible distributions * Random measures * Levy processes * Fractional Brownian motion * Ergodic theory * Karhunen-Loeve expansion * Additional applications * Additional exercises * Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Editio...
Composite stochastic processes
Kampen, N.G. van
Certain problems in physics and chemistry lead to the definition of a class of stochastic processes. Although they are not Markovian they can be treated explicitly to some extent. In particular, the probability distribution for large times can be found. It is shown to obey a master equation. This
Stochastic processes and quantum theory
International Nuclear Information System (INIS)
Klauder, J.R.
1975-01-01
The author analyses a variety of stochastic processes, namely real time diffusion phenomena, which are analogues of imaginary time quantum theory and convariant imaginary time quantum field theory. He elaborates some standard properties involving probability measures and stochastic variables and considers a simple class of examples. Finally he develops the fact that certain stochastic theories actually exhibit divergences that simulate those of covariant quantum field theory and presents examples of both renormaizable and unrenormalizable behavior. (V.J.C.)
Essentials of stochastic processes
Durrett, Richard
2016-01-01
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...
Yang, Xin; Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan
2016-01-01
This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems.
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.
Strategic WIP Inventory Positioning for Make-to-Order Production with Stochastic Processing Times
Directory of Open Access Journals (Sweden)
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.
On time-dependent diffusion coefficients arising from stochastic processes with memory
Carpio-Bernido, M. Victoria; Barredo, Wilson I.; Bernido, Christopher C.
2017-08-01
Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes.
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.
Contribution to the stochastically studies of space-time dependable hydrological processes
International Nuclear Information System (INIS)
Kjaevski, Ivancho
2002-12-01
One of the fundaments of today's planning and water economy is Science of Hydrology. Science of Hydrology through the history had followed the development of the water management systems. Water management systems, during the time from single-approach evolved to complex and multi purpose systems. The dynamic and development of the today's society contributed for increasing the demand of clean water, and in the same time, the resources of clean water in the nature are reduced. In this kind of conditions, water management systems should resolve problems that are more complicated during managing of water sources. Solving the problems in water management, enable development and applying new methods and technologies in planning and management with water resources and water management systems like: systematical analyses, operational research, hierarchy decisions, expert systems, computer technology etc. Planning and management of water sources needs historical measured data for hydro metrological processes. In our country there are data of hydro metrological processes in period of 50-70, but in some Europe countries there are data more than 100 years. Water economy trends follow the hydro metrological trend research. The basic statistic techniques like sampling, probability distribution function, correlation and regression, are used about one intended and simple water management problems. Solving new problems about water management needs using of space-time stochastic technique, modem mathematical and statistical techniques during simulation and optimization of complex water systems. We need tree phases of development of the techniques to get secure hydrological models: i) Estimate the quality of hydro meteorological data, analyzing of their consistency, and homogeneous; ii) Structural analyze of hydro meteorological processes; iii) Mathematical models for modeling hydro meteorological processes. Very often, the third phase is applied for analyzing and modeling of hydro
Stochastic processes inference theory
Rao, Malempati M
2014-01-01
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
Applied probability and stochastic processes
Sumita, Ushio
1999-01-01
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...
Research in Stochastic Processes.
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
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...
D'Onofrio, Giuseppe; Pirozzi, Enrica
2017-05-01
We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.
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...
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...
Electricity price modeling with stochastic time change
International Nuclear Information System (INIS)
Borovkova, Svetlana; Schmeck, Maren Diane
2017-01-01
In this paper, we develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. This technique allows us to incorporate the characteristic features of electricity prices (such as seasonal volatility, time varying mean reversion and seasonally occurring price spikes) into the model in an elegant and economically justifiable way. The stochastic time change introduces stochastic as well as deterministic (e.g., seasonal) features in the price process' volatility and in the jump component. We specify the base process as a mean reverting jump diffusion and the time change as an absolutely continuous stochastic process with seasonal component. The activity rate of the stochastic time change can be related to the factors that influence supply and demand. Here we use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change, and show that this choice leads to realistic price paths. We derive properties of the resulting price process and develop the model calibration procedure. We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths by Monte Carlo simulations. We show that the simulated price process matches the distributional characteristics of the observed electricity prices in periods of both high and low demand. - Highlights: • We develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. • We incorporate the characteristic features of electricity prices, such as seasonal volatility and spikes into the model. • We use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change • We derive properties of the resulting price process and develop the model calibration procedure. • We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths.
Mathematical statistics and stochastic processes
Bosq, Denis
2013-01-01
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic differential equation model to Prendiville processes
International Nuclear Information System (INIS)
Granita; Bahar, Arifah
2015-01-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution
Phenomenological and ratio bifurcations of a class of discrete time stochastic processes
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
Discrete stochastic processes and applications
Collet, Jean-François
2018-01-01
This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy.
Modelling and application of stochastic processes
1986-01-01
The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...
An introduction to probability and stochastic processes
Melsa, James L
2013-01-01
Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2011-01-01
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d
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...
Stochastic Games for Continuous-Time Jump Processes Under Finite-Horizon Payoff Criterion
Energy Technology Data Exchange (ETDEWEB)
Wei, Qingda, E-mail: weiqd@hqu.edu.cn [Huaqiao University, School of Economics and Finance (China); Chen, Xian, E-mail: chenxian@amss.ac.cn [Peking University, School of Mathematical Sciences (China)
2016-10-15
In this paper we study two-person nonzero-sum games for continuous-time jump processes with the randomized history-dependent strategies under the finite-horizon payoff criterion. The state space is countable, and the transition rates and payoff functions are allowed to be unbounded from above and from below. Under the suitable conditions, we introduce a new topology for the set of all randomized Markov multi-strategies and establish its compactness and metrizability. Then by constructing the approximating sequences of the transition rates and payoff functions, we show that the optimal value function for each player is a unique solution to the corresponding optimality equation and obtain the existence of a randomized Markov Nash equilibrium. Furthermore, we illustrate the applications of our main results with a controlled birth and death system.
On discrete stochastic processes with long-lasting time dependence in the variance
Queirós, S. M. D.
2008-11-01
In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of qm-exponencial, form (eqm=1 x=ex). Specifically, we inspect the self-correlation function of squared random variables as well as the kurtosis. In addition, by numerical procedures, we infer the stationary probability density function of both of the heteroskedastic random variables and the variance, the multiscaling properties, the first-passage times distribution, and the dependence degree. Finally, we introduce an asymmetric variance version of the model that enables us to reproduce the so-called leverage effect in financial markets.
Stochastic Games for Continuous-Time Jump Processes Under Finite-Horizon Payoff Criterion
International Nuclear Information System (INIS)
Wei, Qingda; Chen, Xian
2016-01-01
In this paper we study two-person nonzero-sum games for continuous-time jump processes with the randomized history-dependent strategies under the finite-horizon payoff criterion. The state space is countable, and the transition rates and payoff functions are allowed to be unbounded from above and from below. Under the suitable conditions, we introduce a new topology for the set of all randomized Markov multi-strategies and establish its compactness and metrizability. Then by constructing the approximating sequences of the transition rates and payoff functions, we show that the optimal value function for each player is a unique solution to the corresponding optimality equation and obtain the existence of a randomized Markov Nash equilibrium. Furthermore, we illustrate the applications of our main results with a controlled birth and death system.
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...
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Stochastic processes in mechanical engineering
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
Introduction to stochastic processes
Cinlar, Erhan
2013-01-01
Clear presentation employs methods that recognize computer-related aspects of theory. Topics include expectations and independence, Bernoulli processes and sums of independent random variables, Markov chains, renewal theory, more. 1975 edition.
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)
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 processes and filtering theory
Jazwinski, Andrew H
1970-01-01
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab
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 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 Finance and Behavioral Finance
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 ...
An introduction to stochastic processes with applications to biology
Allen, Linda J S
2010-01-01
An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and the genetics of inbreeding. Because of their rich structure, the text focuses on discrete and continuous time Markov chains and continuous time and state Markov processes.New to the Second EditionA new chapter on stochastic differential equations th
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2012-01-01
This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and
Stationary stochastic processes theory and applications
Lindgren, Georg
2012-01-01
Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued stochastic processesBochner's theorem and the spectral distributionSpectral representation of a stationary processGaussian processesStationary counting processesExercisesLinear Filters - General PropertiesLinear time invariant filtersLinear filters and differential equationsWhite noise in linear systemsLong range dependence, non-integrable spectra, and unstable systemsThe ARMA-familyLinear Filters - Special TopicsThe Hilbert transform and the envelopeThe sampling theoremKarhunen-Loève expansionClassical Ergodic Theory and MixingThe basic ergodic theorem in L2Stationarity and transformationsThe ergodic th...
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)
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....
Stochastic time series analysis of hydrology data for water resources
Sathish, S.; Khadar Babu, S. K.
2017-11-01
The prediction to current publication of stochastic time series analysis in hydrology and seasonal stage. The different statistical tests for predicting the hydrology time series on Thomas-Fiering model. The hydrology time series of flood flow have accept a great deal of consideration worldwide. The concentration of stochastic process areas of time series analysis method are expanding with develop concerns about seasonal periods and global warming. The recent trend by the researchers for testing seasonal periods in the hydrologic flowseries using stochastic process on Thomas-Fiering model. The present article proposed to predict the seasonal periods in hydrology using Thomas-Fiering model.
Factors influencing lysis time stochasticity in bacteriophage λ
Directory of Open Access Journals (Sweden)
Dennehy John J
2011-08-01
Full Text Available Abstract Background Despite identical genotypes and seemingly uniform environments, stochastic gene expression and other dynamic intracellular processes can produce considerable phenotypic diversity within clonal microbes. One trait that provides a good model to explore the molecular basis of stochastic variation is the timing of host lysis by bacteriophage (phage. Results Individual lysis events of thermally-inducible λ lysogens were observed using a temperature-controlled perfusion chamber mounted on an inverted microscope. Both mean lysis time (MLT and its associated standard deviation (SD were estimated. Using the SD as a measure of lysis time stochasticity, we showed that lysogenic cells in controlled environments varied widely in lysis times, and that the level of lysis time stochasticity depended on allelic variation in the holin sequence, late promoter (pR' activity, and host growth rate. In general, the MLT was positively correlated with the SD. Both lower pR' activities and lower host growth rates resulted in larger SDs. Results from premature lysis, induced by adding KCN at different time points after lysogen induction, showed a negative correlation between the timing of KCN addition and lysis time stochasticity. Conclusions Taken together with results published by others, we conclude that a large fraction of λ lysis time stochasticity is the result of random events following the expression and diffusion of the holin protein. Consequently, factors influencing the timing of reaching critical holin concentrations in the cell membrane, such as holin production rate, strongly influence the mean lysis time and the lysis time stochasticity.
Stochastic Simulation of Process Calculi for Biology
Directory of Open Access Journals (Sweden)
Andrew Phillips
2010-10-01
Full Text Available Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed, many of which are expressive enough to generate unbounded numbers of molecular species and reactions. As a result of this expressiveness, such calculi cannot rely on standard reaction-based simulation methods, which require fixed numbers of species and reactions. Rather than implementing custom stochastic simulation algorithms for each process calculus, we propose to use a generic abstract machine that can be instantiated to a range of process calculi and a range of reaction-based simulation algorithms. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. In this short paper we give a brief summary of the generic abstract machine, and show how it can be instantiated with the stochastic simulation algorithm known as Gillespie's Direct Method. We also discuss the wider implications of such an abstract machine, and outline how it can be used to simulate multiple calculi simultaneously within a common framework.
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...
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.
Stationary stochastic processes for scientists and engineers
Lindgren, Georg; Sandsten, Maria
2013-01-01
""This book is designed for a first course in stationary stochastic processes in science and engineering and does a very good job in introducing many concepts and ideas to students in these fields. … the book has probably been tested in the classroom many times, which also manifests itself in its virtual lack of typos. … Another great feature of the book is that it contains a wealth of worked example from many different fields. These help clarify concepts and theorems and I believe students will appreciate them-I certainly did. … The book is well suited for a one-semester course as it contains
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
Stochastic Processes in Epidemic Theory
Lefèvre, Claude; Picard, Philippe
1990-01-01
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
Towards Model Checking Stochastic Process Algebra
Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.
2000-01-01
Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of
Stochastic 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)
Stochastic first passage time accelerated with CUDA
Pierro, Vincenzo; Troiano, Luigi; Mejuto, Elena; Filatrella, Giovanni
2018-05-01
The numerical integration of stochastic trajectories to estimate the time to pass a threshold is an interesting physical quantity, for instance in Josephson junctions and atomic force microscopy, where the full trajectory is not accessible. We propose an algorithm suitable for efficient implementation on graphical processing unit in CUDA environment. The proposed approach for well balanced loads achieves almost perfect scaling with the number of available threads and processors, and allows an acceleration of about 400× with a GPU GTX980 respect to standard multicore CPU. This method allows with off the shell GPU to challenge problems that are otherwise prohibitive, as thermal activation in slowly tilted potentials. In particular, we demonstrate that it is possible to simulate the switching currents distributions of Josephson junctions in the timescale of actual experiments.
Selected papers on noise and stochastic processes
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
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
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...
Forecasting financial asset processes: stochastic dynamics via learning neural networks.
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.
Is human failure a stochastic process?
International Nuclear Information System (INIS)
Dougherty, Ed M.
1997-01-01
Human performance results in failure events that occur with a risk-significant frequency. System analysts have taken for granted the random (stochastic) nature of these events in engineering assessments such as risk assessment. However, cognitive scientists and error technologists, at least those who have interest in human reliability, have, over the recent years, claimed that human error does not need this stochastic framework. Yet they still use the language appropriate to stochastic processes. This paper examines the potential for the stochastic nature of human failure production as the basis for human reliability analysis. It distinguishes and leaves to others, however, the epistemic uncertainties over the possible probability models for the real variability of human performance
Stochastic 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.
Stochastic models for time series
Doukhan, Paul
2018-01-01
This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit ...
Lectures on Topics in Spatial Stochastic Processes
Capasso, Vincenzo; Ivanoff, B Gail; Dozzi, Marco; Dalang, Robert C; Mountford, Thomas S
2003-01-01
The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.
Reversibility in Quantum Models of Stochastic Processes
Gier, David; Crutchfield, James; Mahoney, John; James, Ryan
Natural phenomena such as time series of neural firing, orientation of layers in crystal stacking and successive measurements in spin-systems are inherently probabilistic. The provably minimal classical models of such stochastic processes are ɛ-machines, which consist of internal states, transition probabilities between states and output values. The topological properties of the ɛ-machine for a given process characterize the structure, memory and patterns of that process. However ɛ-machines are often not ideal because their statistical complexity (Cμ) is demonstrably greater than the excess entropy (E) of the processes they represent. Quantum models (q-machines) of the same processes can do better in that their statistical complexity (Cq) obeys the relation Cμ >= Cq >= E. q-machines can be constructed to consider longer lengths of strings, resulting in greater compression. With code-words of sufficiently long length, the statistical complexity becomes time-symmetric - a feature apparently novel to this quantum representation. This result has ramifications for compression of classical information in quantum computing and quantum communication technology.
Topological superposition of abstractions of stochastic processes
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
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.
Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes
Williams Colin P.
1999-01-01
Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.
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
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....
ON REGRESSION REPRESENTATIONS OF STOCHASTIC-PROCESSES
RUSCHENDORF, L; DEVALK, [No Value
We construct a.s. nonlinear regression representations of general stochastic processes (X(n))n is-an-element-of N. As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive
Stochastic transport processes in discrete biological systems
Frehland, Eckart
1982-01-01
These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz. These notes contain the results of re cent studies on the stochastic description of ion transport through biological membranes. In particular, they serve as an introduction to an unified theory of fluctuations in complex biological transport systems. We emphasize that the subject of this volume is not to introduce the mathematics of stochastic processes but to present a field of theoretical biophysics in which stochastic methods are important. In the last years the study of membrane noise has become an important method in biophysics. Valuable information on the ion transport mechanisms in membranes can be obtained from noise analysis. A number of different processes such as the opening and closing of ion channels have been shown to be sources of the measured current or voltage fluctuations. Bio logical 'transport systems can be complex. For example, the tr...
Anomalous scaling of stochastic processes and the Moses effect.
Chen, Lijian; Bassler, Kevin E; McCauley, Joseph L; Gunaratne, Gemunu H
2017-04-01
The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t^{1/2}. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.
Anomalous scaling of stochastic processes and the Moses effect
Chen, Lijian; Bassler, Kevin E.; McCauley, Joseph L.; Gunaratne, Gemunu H.
2017-04-01
The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t1/2. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.
Stochastic calculus for uncoupled continuous-time random walks.
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L
2009-06-01
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy alpha -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.
Stochastic processes and applications diffusion processes, the Fokker-Planck and Langevin equations
Pavliotis, Grigorios A
2014-01-01
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to eq...
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)
Periodic linear differential stochastic processes
Kwakernaak, H.
1975-01-01
Periodic linear differential processes are defined and their properties are analyzed. Equivalent representations are discussed, and the solutions of related optimal estimation problems are given. An extension is presented of Kailath and Geesey’s [1] results concerning the innovations representation
Stochastic nature of series of waiting times
Anvari, Mehrnaz; Aghamohammadi, Cina; Dashti-Naserabadi, H.; Salehi, E.; Behjat, E.; Qorbani, M.; Khazaei Nezhad, M.; Zirak, M.; Hadjihosseini, Ali; Peinke, Joachim; Tabar, M. Reza Rahimi
2013-06-01
Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the “waiting times” series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2
Irreversible stochastic processes on lattices
International Nuclear Information System (INIS)
Nord, R.S.
1986-01-01
Models for irreversible random or cooperative filling of lattices are required to describe many processes in chemistry and physics. Since the filling is assumed to be irreversible, even the stationary, saturation state is not in equilibrium. The kinetics and statistics of these processes are described by recasting the master equations in infinite hierarchical form. Solutions can be obtained by implementing various techniques: refinements in these solution techniques are presented. Programs considered include random dimer, trimer, and tetramer filling of 2D lattices, random dimer filling of a cubic lattice, competitive filling of two or more species, and the effect of a random distribution of inactive sites on the filling. Also considered is monomer filling of a linear lattice with nearest neighbor cooperative effects and solve for the exact cluster-size distribution for cluster sizes up to the asymptotic regime. Additionally, a technique is developed to directly determine the asymptotic properties of the cluster size distribution. Finally cluster growth is considered via irreversible aggregation involving random walkers. In particular, explicit results are provided for the large-lattice-size asymptotic behavior of trapping probabilities and average walk lengths for a single walker on a lattice with multiple traps. Procedures for exact calculation of these quantities on finite lattices are also developed
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...
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)
Stochastic ℋ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.
A compositional Translation of Stochastic Automata into Timed Automata
d' Argenio, P.R.
We present a translation from stochastic automata [17, 16] into timed automata with deadlines [37, 13]. The translation preserves traces when the stochastic characteristics, namely the probability measures, are abstracted from the original stochastic automaton. Moreover, we show that the translation
Minimum uncertainty and squeezing in diffusion processes and stochastic quantization
Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe
1994-01-01
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
Doubly stochastic Poisson processes in artificial neural learning.
Card, H C
1998-01-01
This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.
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...
Vehicle routing with stochastic time-dependent travel times
Lecluyse, C.; Woensel, van T.; Peremans, H.
2009-01-01
Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the
Vehicle routing with stochastic time-dependent travel times
Lecluyse, C.; Woensel, van T.; Peremans, H.
2007-01-01
Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the
Stochastic analysis in production process and ecology under uncertainty
Bieda, Bogusław
2014-01-01
The monograph addresses a problem of stochastic analysis based on the uncertainty assessment by simulation and application of this method in ecology and steel industry under uncertainty. The first chapter defines the Monte Carlo (MC) method and random variables in stochastic models. Chapter two deals with the contamination transport in porous media. Stochastic approach for Municipal Solid Waste transit time contaminants modeling using MC simulation has been worked out. The third chapter describes the risk analysis of the waste to energy facility proposal for Konin city, including the financial aspects. Environmental impact assessment of the ArcelorMittal Steel Power Plant, in Kraków - in the chapter four - is given. Thus, four scenarios of the energy mix production processes were studied. Chapter five contains examples of using ecological Life Cycle Assessment (LCA) - a relatively new method of environmental impact assessment - which help in preparing pro-ecological strategy, and which can lead to reducing t...
Learning Theory Estimates with Observations from General Stationary Stochastic Processes.
Hang, Hanyuan; Feng, Yunlong; Steinwart, Ingo; Suykens, Johan A K
2016-12-01
This letter investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by general, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established. The obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization (ERM), least squares support vector machines (LS-SVMs) using given generic kernels, and SVMs using gaussian kernels for both least squares and quantile regression. It turns out that for independent and identically distributed (i.i.d.) processes, our learning rates for ERM recover the optimal rates. For non-i.i.d. processes, including geometrically [Formula: see text]-mixing Markov processes, geometrically [Formula: see text]-mixing processes with restricted decay, [Formula: see text]-mixing processes, and (time-reversed) geometrically [Formula: see text]-mixing processes, our learning rates for SVMs with gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates. For the remaining cases, our rates are at least close to the optimal rates. As a by-product, the assumed generalized Bernstein-type inequality also provides an interpretation of the so-called effective number of observations for various mixing processes.
A first course in stochastic processes
Karlin, Samuel
1975-01-01
The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other.The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processe
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.
XI Symposium on Probability and Stochastic Processes
Pardo, Juan; Rivero, Víctor; Bravo, Gerónimo
2015-01-01
This volume features lecture notes and a collection of contributed articles from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since the symposium was part of the activities organized in Mexico to celebrate the International Year of Statistics, the program included topics from the interface between statistics and stochastic processes. The book starts with notes from the mini-course given by Louigi Addario-Berry with an accessible description of some features of the multiplicative coalescent and its connection with random graphs and minimum spanning trees. It includes a number of exercises and a section on unanswered questions. Further contributions provide the reader with a broad perspective on the state-of-the art of active areas of research. Contributions by: Louigi Addario-Berry Octavio Arizmendi Fabrice Baudoin Jochen Blath Loïc Chaumont J. Armando Domínguez-Molina Bjarki Eldon Shui Feng Tulio Gaxiola Adrián González Casanova Evgueni Gordienko Daniel...
Quantum dynamical time evolutions as stochastic flows on phase space
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Guerra, F.; Sirigue, M.; Sirigue-Collin, M.
1984-01-01
We are mainly interested in describing the time development of the Wigner functions by means of stochastic processes. In the second section we recall the main properties of the Wigner functions as well as those of their Fourier transform. In the next one we derive the evolution equation of these functions for a class of Hamiltonians and we give a probabilistic expression for the solution of these equations by means of a stochastic flow in phase space which reminds of the classical flows. In the last section we remark that the previously defined flow can be extended to the bounded continuous functions on phase space and that this flow conserves the cone generated by the Wigner functions. (orig./HSI)
Stochastic processes from physics to finance
Paul, Wolfgang
2013-01-01
This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.
Simulation of anaerobic digestion processes using stochastic algorithm.
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 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.
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.)
Stochastic processes dominate during boreal bryophyte community assembly.
Fenton, Nicole J; Bergeron, Yves
2013-09-01
Why are plant species found in certain locations and not in others? The study of community assembly rules has attempted to answer this question, and many studies articulate the historic dichotomy of deterministic (predictable niches) vs. stochastic (random or semi-random processes). The study of successional sequences to determine whether they converge, as would be expected by deterministic theory, or diverge, as stochastic theory would suggest, has been one method used to investigate this question. In this article we ask the question: Do similar boreal bryophyte communities develop in the similar habitat created by convergent succession after fires of different severities? Or do the stochastic processes generated by fires of different severity lead to different communities? Specifically we predict that deterministic structure will be more important for large forest-floor species than stochastic processes, and that the inverse will be true for small bryophyte species. We used multivariate regression trees and model selection to determine the relative weight of structure (forest structure, substrates, soil structure) and processes (fire severity) for two groups of bryophyte species sampled in 12 sites (seven high-severity and five low-severity fires). Contrary to our first hypothesis, processes were as important for large forest-floor bryophytes as for small pocket species. Fire severity, its interaction with the quality of available habitat, and its impact on the creation of biological legacies played dominant roles in determining community structure. In this study, sites with nearly identical forest structure, generated via convergent succession after high- and low-severity fire, were compared to see whether these sites supported similar bryophyte communities. While similar to some degree, both the large forest-floor species and the pocket species differed after high-severity fire compared to low-severity fire. This result suggests that the "how," or process of
Chemical kinetics, stochastic processes, and irreversible thermodynamics
Santillán, Moisés
2014-01-01
This book brings theories in nonlinear dynamics, stochastic processes, irreversible thermodynamics, physical chemistry, and biochemistry together in an introductory but formal and comprehensive manner. Coupled with examples, the theories are developed stepwise, starting with the simplest concepts and building upon them into a more general framework. Furthermore, each new mathematical derivation is immediately applied to one or more biological systems. The last chapters focus on applying mathematical and physical techniques to study systems such as: gene regulatory networks and ion channels. The target audience of this book are mainly final year undergraduate and graduate students with a solid mathematical background (physicists, mathematicians, and engineers), as well as with basic notions of biochemistry and cellular biology. This book can also be useful to students with a biological background who are interested in mathematical modeling, and have a working knowledge of calculus, differential equatio...
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.
Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process
Turner, Douglas C.; Ladde, Gangaram S.
2018-03-01
Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.
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...
Process theory for supervisory control of stochastic systems with data
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
Stochastic processes and long range dependence
Samorodnitsky, Gennady
2016-01-01
This monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory). The text is organized around the probabilistic properties of stationary processes that are important for determining the presence or absence of long memory. The first few chapters serve as an overview of the general theory of stochastic processes which gives the reader sufficient background, language, and models for the subsequent discussion of long memory. The later chapters devoted to long memory begin with an introduction to the subject along with a brief history of its development, followed by a presentation of what is currently the best known approach, applicable to stationary processes with a finite second moment. The book concludes with a chapter devoted to the author’s own, less standard, point of view of long memory as a phase transition, and even includes some novel results. Most of the material in the book has not previously been publis...
Stochastic differential equations and diffusion processes
Ikeda, N
1989-01-01
Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sectio
Multiple-scale stochastic processes: Decimation, averaging and beyond
Energy Technology Data Exchange (ETDEWEB)
Bo, Stefano, E-mail: stefano.bo@nordita.org [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Celani, Antonio [Quantitative Life Sciences, The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 - Trieste (Italy)
2017-02-07
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This has provided fruitful applications for established stochastic methods and motivated further developments. These systems often involve processes taking place on widely separated time scales. For an efficient modeling one usually focuses on the slower degrees of freedom and it is of great importance to accurately eliminate the fast variables in a controlled fashion, carefully accounting for their net effect on the slower dynamics. This procedure in general requires to perform two different operations: decimation and coarse-graining. We introduce the asymptotic methods that form the basis of this procedure and discuss their application to a series of physical, biological and chemical examples. We then turn our attention to functionals of the stochastic trajectories such as residence times, counting statistics, fluxes, entropy production, etc. which have been increasingly studied in recent years. For such functionals, the elimination of the fast degrees of freedom can present additional difficulties and naive procedures can lead to blatantly inconsistent results. Homogenization techniques for functionals are less covered in the literature and we will pedagogically present them here, as natural extensions of the ones employed for the trajectories. We will also discuss recent applications of these techniques to the thermodynamics of small systems and their interpretation in terms of information-theoretic concepts.
On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.
International Nuclear Information System (INIS)
Granita; Bahar, A.
2015-01-01
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)
2015-03-09
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.
American option pricing with stochastic volatility processes
Directory of Open Access Journals (Sweden)
Ping LI
2017-12-01
Full Text Available In order to solve the problem of option pricing more perfectly, the option pricing problem with Heston stochastic volatility model is considered. The optimal implementation boundary of American option and the conditions for its early execution are analyzed and discussed. In view of the fact that there is no analytical American option pricing formula, through the space discretization parameters, the stochastic partial differential equation satisfied by American options with Heston stochastic volatility is transformed into the corresponding differential equations, and then using high order compact finite difference method, numerical solutions are obtained for the option price. The numerical experiments are carried out to verify the theoretical results and simulation. The two kinds of optimal exercise boundaries under the conditions of the constant volatility and the stochastic volatility are compared, and the results show that the optimal exercise boundary also has stochastic volatility. Under the setting of parameters, the behavior and the nature of volatility are analyzed, the volatility curve is simulated, the calculation results of high order compact difference method are compared, and the numerical option solution is obtained, so that the method is verified. The research result provides reference for solving the problems of option pricing under stochastic volatility such as multiple underlying asset option pricing and barrier option pricing.
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...
Soil Erosion as a stochastic process
Casper, Markus C.
2015-04-01
corrected experimentally. To overcome this disadvantage of our actual models, soil erosion models are needed that are able to use stochastic directly variables and parameter distributions. There are only some minor approaches in this direction. The most advanced is the model "STOSEM" proposed by Sidorchuk in 2005. In this model, only a small part of the soil erosion processes is described, the aggregate detachment and the aggregate transport by flowing water. The concept is highly simplified, for example, many parameters are temporally invariant. Nevertheless, the main problem is that our existing measurements and experiments are not geared to provide stochastic parameters (e.g. as probability density functions); in the best case they deliver a statistical validation of the mean values. Again, we get effective parameters, spatially and temporally averaged. There is an urgent need for laboratory and field experiments on overland flow structure, raindrop effects and erosion rate, which deliver information on spatial and temporal structure of soil and surface properties and processes.
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.
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)
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...
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
Introduction to probability and stochastic processes with applications
Castañ, Blanco; Arunachalam, Viswanathan; Dharmaraja, Selvamuthu
2012-01-01
An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic t
Evoking prescribed spike times in stochastic neurons
Doose, Jens; Lindner, Benjamin
2017-09-01
Single cell stimulation in vivo is a powerful tool to investigate the properties of single neurons and their functionality in neural networks. We present a method to determine a cell-specific stimulus that reliably evokes a prescribed spike train with high temporal precision of action potentials. We test the performance of this stimulus in simulations for two different stochastic neuron models. For a broad range of parameters and a neuron firing with intermediate firing rates (20-40 Hz) the reliability in evoking the prescribed spike train is close to its theoretical maximum that is mainly determined by the level of intrinsic noise.
An extension of clarke's model with stochastic amplitude flip processes
Hoel, Hakon
2014-07-01
Stochastic modeling is an essential tool for studying statistical properties of wireless channels. In multipath fading channel (MFC) models, the signal reception is modeled by a sum of wave path contributions, and Clarke\\'s model is an important example of such which has been widely accepted in many wireless applications. However, since Clarke\\'s model is temporally deterministic, Feng and Field noted that it does not model real wireless channels with time-varying randomness well. Here, we extend Clarke\\'s model to a novel time-varying stochastic MFC model with scatterers randomly flipping on and off. Statistical properties of the MFC model are analyzed and shown to fit well with real signal measurements, and a limit Gaussian process is derived from the model when the number of active wave paths tends to infinity. A second focus of this work is a comparison study of the error and computational cost of generating signal realizations from the MFC model and from its limit Gaussian process. By rigorous analysis and numerical studies, we show that in many settings, signal realizations are generated more efficiently by Gaussian process algorithms than by the MFC model\\'s algorithm. Numerical examples that strengthen these observations are also presented. © 2014 IEEE.
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)
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...
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...
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
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...
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
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 ...
Bidirectional Classical Stochastic Processes with Measurements and Feedback
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.
Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.
García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G
2017-08-01
The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.
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
Approximation of itô integrals arising in stochastic time-delayed systems
Bagchi, Arunabha
1984-01-01
Likelihood functional for stochastic linear time-delayed systems involve Itô integrals with respect to the observed data. Since the Wiener process appearing in the standard observation process model for such systems is not realizable and the physically observed process is smooth, one needs to study
Stochastic Analysis of Gaussian Processes via Fredholm Representation
Directory of Open Access Journals (Sweden)
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.
Evolution and mass extinctions as lognormal stochastic processes
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
Stochastic Modelling of Shiroro River Stream flow Process
Musa, J. J
2013-01-01
Economists, social scientists and engineers provide insights into the drivers of anthropogenic climate change and the options for adaptation and mitigation, and yet other scientists, including geographers and biologists, study the impacts of climate change. This project concentrates mainly on the discharge from the Shiroro River. A stochastic approach is presented for modeling a time series by an Autoregressive Moving Average model (ARMA). The development and use of a stochastic stream flow m...
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
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
Diffusive processes in a stochastic magnetic field
International Nuclear Information System (INIS)
Wang, H.; Vlad, M.; Vanden Eijnden, E.; Spineanu, F.; Misguich, J.H.; Balescu, R.
1995-01-01
The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle's trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works
Simulating biological processes: stochastic physics from whole cells to colonies
Earnest, Tyler M.; Cole, John A.; Luthey-Schulten, Zaida
2018-05-01
The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a ‘minimal cell’. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.
Time-Weighted Balanced Stochastic Model Reduction
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2011-01-01
A new relative error model reduction technique for linear time invariant (LTI) systems is proposed in this paper. Both continuous and discrete time systems can be reduced within this framework. The proposed model reduction method is mainly based upon time-weighted balanced truncation and a recently...
Single-molecule stochastic times in a reversible bimolecular reaction
Keller, Peter; Valleriani, Angelo
2012-08-01
In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.
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)
The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates
Directory of Open Access Journals (Sweden)
Yilun Shang
2013-01-01
Full Text Available We investigate a variant of the stochastic logistic model that allows individual variation and time-dependent infection and recovery rates. The model is described as a heterogeneous density dependent Markov chain. We show that the process can be approximated by a deterministic process defined by an integral equation as the population size grows.
Suzuki, Yuichi; Nagaoka, Masataka
2017-05-28
Atomistic information of a whole chemical reaction system, e.g., instantaneous microscopic molecular structures and orientations, offers important and deeper insight into clearly understanding unknown chemical phenomena. In accordance with the progress of a number of simultaneous chemical reactions, the Red Moon method (a hybrid Monte Carlo/molecular dynamics reaction method) is capable of simulating atomistically the chemical reaction process from an initial state to the final one of complex chemical reaction systems. In the present study, we have proposed a transformation theory to interpret the chemical reaction process of the Red Moon methodology as the time evolution process in harmony with the chemical kinetics. For the demonstration of the theory, we have chosen the gas reaction system in which the reversible second-order reaction H 2 + I 2 ⇌ 2HI occurs. First, the chemical reaction process was simulated from the initial configurational arrangement containing a number of H 2 and I 2 molecules, each at 300 K, 500 K, and 700 K. To reproduce the chemical equilibrium for the system, the collision frequencies for the reactions were taken into consideration in the theoretical treatment. As a result, the calculated equilibrium concentrations [H 2 ] eq and equilibrium constants K eq at all the temperatures were in good agreement with their corresponding experimental values. Further, we applied the theoretical treatment for the time transformation to the system and have shown that the calculated half-life τ's of [H 2 ] reproduce very well the analytical ones at all the temperatures. It is, therefore, concluded that the application of the present theoretical treatment with the Red Moon method makes it possible to analyze reasonably the time evolution of complex chemical reaction systems to chemical equilibrium at the atomistic level.
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
Classical and spatial stochastic processes with applications to biology
Schinazi, Rinaldo B
2014-01-01
The revised and expanded edition of this textbook presents the concepts and applications of random processes with the same illuminating simplicity as its first edition, but with the notable addition of substantial modern material on biological modeling. While still treating many important problems in fields such as engineering and mathematical physics, the book also focuses on the highly relevant topics of cancerous mutations, influenza evolution, drug resistance, and immune response. The models used elegantly apply various classical stochastic models presented earlier in the text, and exercises are included throughout to reinforce essential concepts. The second edition of Classical and Spatial Stochastic Processes is suitable as a textbook for courses in stochastic processes at the advanced-undergraduate and graduate levels, or as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology. Reviews of the first edition: An appetizing textbook for a f...
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.
A measure theoretical approach to quantum stochastic processes
Von Waldenfels, Wilhelm
2014-01-01
This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. Considering in detail four basic examples (e.g. a two-level atom coupled to a heat bath of oscillators), in each case the Hamiltonian of the associated one-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors. Advanced topics include the theory of the Hudson-Parthasarathy equation and the amplified oscillator problem. To that end, a chapter on white noise calculus has also been included.
? filtering for stochastic systems driven by Poisson processes
Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya
2015-01-01
This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.
A Constructive Sharp Approach to Functional Quantization of Stochastic Processes
Junglen, Stefan; Luschgy, Harald
2010-01-01
We present a constructive approach to the functional quantization problem of stochastic processes, with an emphasis on Gaussian processes. The approach is constructive, since we reduce the infinite-dimensional functional quantization problem to a finite-dimensional quantization problem that can be solved numerically. Our approach achieves the sharp rate of the minimal quantization error and can be used to quantize the path space for Gaussian processes and also, for example, Lévy processes.
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.
Gene regulation and noise reduction by coupling of stochastic processes
Ramos, Alexandre F.; Hornos, José Eduardo M.; Reinitz, John
2015-02-01
Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.
Gene regulation and noise reduction by coupling of stochastic processes.
Ramos, Alexandre F; Hornos, José Eduardo M; Reinitz, John
2015-02-01
Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.
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...
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; ...
Modified stochastic fragmentation of an interval as an ageing process
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.
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
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.
Uncertainty Reduction for Stochastic Processes on Complex Networks
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.
Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time
Dhar, Amrit
2017-01-01
Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780
A 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...
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
Empirical method to measure stochasticity and multifractality in nonlinear time series
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.
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.
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.
Deterministic geologic processes and stochastic modeling
International Nuclear Information System (INIS)
Rautman, C.A.; Flint, A.L.
1992-01-01
This paper reports that recent outcrop sampling at Yucca Mountain, Nevada, has produced significant new information regarding the distribution of physical properties at the site of a potential high-level nuclear waste repository. consideration of the spatial variability indicates that her are a number of widespread deterministic geologic features at the site that have important implications for numerical modeling of such performance aspects as ground water flow and radionuclide transport. Because the geologic processes responsible for formation of Yucca Mountain are relatively well understood and operate on a more-or-less regional scale, understanding of these processes can be used in modeling the physical properties and performance of the site. Information reflecting these deterministic geologic processes may be incorporated into the modeling program explicitly using geostatistical concepts such as soft information, or implicitly, through the adoption of a particular approach to modeling
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
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.
Stochasticity in processes fundamentals and applications to chemistry and biology
Schuster, Peter
2016-01-01
This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic collection of the mathematical background material needed to understand probability, statistics, and stochastic processes as a prerequisite for the increasingly challenging practical applications in chemistry and the life sciences examined in the second part. Recent advances in the development of new techniques and in the resolution of conventional experiments at nano-scales have been tremendous: today molecular spectroscopy can provide insights into processes down to scales at which current theories at the interface of physics, chemistry and the life sciences cannot be successful without a firm grasp of randomness and its sources. Routinely measured data is now sufficiently accurate to allow the direct recording of fluctuations. As a result, the sampling of data and the modeling of relevant processes are doomed t...
Stochastic Models in the Identification Process
Czech Academy of Sciences Publication Activity Database
Slovák, Dalibor; Zvárová, Jana
2011-01-01
Roč. 7, č. 1 (2011), s. 44-50 ISSN 1801-5603 R&D Projects: GA MŠk(CZ) 1M06014 Institutional research plan: CEZ:AV0Z10300504 Keywords : identification process * weight-of evidence formula * coancestry coefficient * beta-binomial sampling formula * DNA mixtures Subject RIV: IN - Informatics, Computer Science http://www.ejbi.eu/images/2011-1/Slovak_en.pdf
ℋ∞ constant gain state feedback stabilization of stochastic hybrid systems with Wiener process
Directory of Open Access Journals (Sweden)
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.
5th Seminar on Stochastic Processes, Random Fields and Applications
Russo, Francesco; Dozzi, Marco
2008-01-01
This volume contains twenty-eight refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 30 to June 3, 2005. The seminar focused mainly on stochastic partial differential equations, random dynamical systems, infinite-dimensional analysis, approximation problems, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance. Contributors: Y. Asai, J.-P. Aubin, C. Becker, M. Benaïm, H. Bessaih, S. Biagini, S. Bonaccorsi, N. Bouleau, N. Champagnat, G. Da Prato, R. Ferrière, F. Flandoli, P. Guasoni, V.B. Hallulli, D. Khoshnevisan, T. Komorowski, R. Léandre, P. Lescot, H. Lisei, J.A. López-Mimbela, V. Mandrekar, S. Méléard, A. Millet, H. Nagai, A.D. Neate, V. Orlovius, M. Pratelli, N. Privault, O. Raimond, M. Röckner, B. Rüdiger, W.J. Runggaldi...
Discrete stochastic processes and optimal filtering
Bertein, Jean-Claude
2012-01-01
Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which ar
Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process
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.
Reconstruction theorem for a quantum stochastic process
International Nuclear Information System (INIS)
Belavkin, V.P.
1985-01-01
This paper gives a physically interpretable--in real time--definition of a QSP as families of representations of the observable algebra 'B' in a common (large) system by indicating a universal method of constructing such a system from casual correlation operators described by the axioms formulated in the paper. The authors encompass in a unified manner both nonrelativistic and relativistic covariant QSPs describing open quantum systems and fields in a causally ordered region accessible to observation. The principle of nondestruction by successive measurements of a QSP of a given quantum subsystem is also taken into account
Infinite time interval backward stochastic differential equations with continuous coefficients.
Zong, Zhaojun; Hu, Feng
2016-01-01
In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).
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
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.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Energy Technology Data Exchange (ETDEWEB)
Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)
2012-03-15
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
International Nuclear Information System (INIS)
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-01-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-03-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
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...
Bridging time scales in cellular decision making with a stochastic bistable switch
Directory of Open Access Journals (Sweden)
Waldherr Steffen
2010-08-01
Full Text Available Abstract Background Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. Some of these transformations act over a very long time scale on the cell population level, up to the entire lifespan of the organism. Results In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Conclusions Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.
Stochastic Approach to Determine CO2 Hydrate Induction Time in Clay Mineral Suspensions
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.
Beam life-time with intrabeam scattering and stochastic cooling
International Nuclear Information System (INIS)
Wei, J.; Ruggiero, A.G.
1991-01-01
A transport equation has been derived in terms of the longitudinal action variable to describe the time evolution of the longitudinal density distribution of a bunched hadron beam in the presence of intrabeam scattering and stochastic cooling. A computer program has been developed to numerically solve this equation. Both beam loss and bunch-shape evolution have been investigated for the 197 Au 79+ beams during the 10-hour storage in the Relativistic Heavy Ion Collider currently under construction at the Brookhaven National Laboratory. 9 refs., 1 fig
Random migration processes between two stochastic epidemic centers.
Sazonov, Igor; Kelbert, Mark; Gravenor, Michael B
2016-04-01
We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically. Copyright © 2016 Elsevier Inc. All rights reserved.
Stochastic 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)
Quantitative Sociodynamics Stochastic Methods and Models of Social Interaction Processes
Helbing, Dirk
2010-01-01
This new edition of Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioral changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics and mathematics, but they have very often proven their explanatory power in chemistry, biology, economics and the social sciences as well. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces important concepts from nonlinear dynamics (e.g. synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches, a fundamental dynamic model is obtained, which opens new perspectives in the social sciences. It includes many established models a...
Quantitative sociodynamics stochastic methods and models of social interaction processes
Helbing, Dirk
1995-01-01
Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioural changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics but they have very often proved their explanatory power in chemistry, biology, economics and the social sciences. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces the most important concepts from nonlinear dynamics (synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches a very fundamental dynamic model is obtained which seems to open new perspectives in the social sciences. It includes many established models as special cases, e.g. the log...
Stochastic Landau equation with time-dependent drift
International Nuclear Information System (INIS)
Swift, J.B.; Hohenberg, P.C.; Ahlers, G.
1991-01-01
The stochastic differential equation τ 0 ∂ tA =ε(t)A-g 3 A 3 +bar f(t), where bar f(t) is Gaussian white noise, is studied for arbitrary time dependence of ε(t). In particular, cases are considered where ε(t) goes through the bifurcation of the deterministic system, which occurs at ε=0. In the limit of weak noise an approximate analytic expression generalizing earlier work of Suzuki [Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) Suppl. 64, 402 (1978)] is obtained for the time-dependent distribution function P(A,t). The results compare favorably with a numerical simulation of the stochastic equation for the case of a linear ramp (both increasing and decreasing) and for a periodic time dependence of ε(t). The procedure can be generalized to an arbitrary deterministic part ∂ tA =D(A,t)+bar f(t), but the deterministic equation may then have to be solved numerically
Directory of Open Access Journals (Sweden)
Xueling Jiang
2014-01-01
Full Text Available The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and the M-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.
Detecting stochastic backgrounds of gravitational waves with pulsar timing arrays
Siemens, Xavier
2016-03-01
For the past decade the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has been using the Green Bank Telescope and the Arecibo Observatory to monitor millisecond pulsars. NANOGrav, along with two other international collaborations, the European Pulsar Timing Array and the Parkes Pulsar Timing Array in Australia, form a consortium of consortia: the International Pulsar Timing Array (IPTA). The goal of the IPTA is to directly detect low-frequency gravitational waves which cause small changes to the times of arrival of radio pulses from millisecond pulsars. In this talk I will discuss the work of NANOGrav and the IPTA, as well as our sensitivity to stochastic backgrounds of gravitational waves. I will show that a detection of the background produced by supermassive black hole binaries is possible by the end of the decade. Supported by the NANOGrav Physics Frontiers Center.
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...
Absolute continuity under time shift of trajectories and related stochastic calculus
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|\
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...
Extensions of Statecharts with probability, time, and stochastic timing
Jansen, D.N.
2003-01-01
Statecharts are a graphical language to describe the behaviour of a (computer) system. Statecharts are, among others, used as a part of the UML (Unified Modelling Language). This thesis describes three extensions related to statecharts. One of them is a real-time property language that fits well
A decision dependent stochastic process model for repairable systems with applications
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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.
Population density equations for stochastic processes with memory kernels
Lai, Yi Ming; de Kamps, Marc
2017-06-01
We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.
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...
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...
Simulation of Stochastic Processes by Coupled ODE-PDE
Zak, Michail
2008-01-01
A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.
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.
ARMA modelling of neutron stochastic processes with large measurement noise
International Nuclear Information System (INIS)
Zavaljevski, N.; Kostic, Lj.; Pesic, M.
1994-01-01
An autoregressive moving average (ARMA) model of the neutron fluctuations with large measurement noise is derived from langevin stochastic equations and validated using time series data obtained during prompt neutron decay constant measurements at the zero power reactor RB in Vinca. Model parameters are estimated using the maximum likelihood (ML) off-line algorithm and an adaptive pole estimation algorithm based on the recursive prediction error method (RPE). The results show that subcriticality can be determined from real data with high measurement noise using much shorter statistical sample than in standard methods. (author)
Unifying three perspectives on information processing in stochastic thermodynamics.
Barato, A C; Seifert, U
2014-03-07
So far, feedback-driven systems have been discussed using (i) measurement and control, (ii) a tape interacting with a system, or (iii) by identifying an implicit Maxwell demon in steady-state transport. We derive the corresponding second laws from one master fluctuation theorem and discuss their relationship. In particular, we show that both the entropy production involving mutual information between system and controller and the one involving a Shannon entropy difference of an information reservoir like a tape carry an extra term different from the usual current times affinity. We, thus, generalize stochastic thermodynamics to the presence of an information reservoir.
Stationary and related stochastic processes sample function properties and their applications
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
Real-Time Demand Side Management Algorithm Using Stochastic Optimization
Directory of Open Access Journals (Sweden)
Moses Amoasi Acquah
2018-05-01
Full Text Available A demand side management technique is deployed along with battery energy-storage systems (BESS to lower the electricity cost by mitigating the peak load of a building. Most of the existing methods rely on manual operation of the BESS, or even an elaborate building energy-management system resorting to a deterministic method that is susceptible to unforeseen growth in demand. In this study, we propose a real-time optimal operating strategy for BESS based on density demand forecast and stochastic optimization. This method takes into consideration uncertainties in demand when accounting for an optimal BESS schedule, making it robust compared to the deterministic case. The proposed method is verified and tested against existing algorithms. Data obtained from a real site in South Korea is used for verification and testing. The results show that the proposed method is effective, even for the cases where the forecasted demand deviates from the observed demand.
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.
Stochastic models for structured populations scaling limits and long time behavior
Meleard, Sylvie
2015-01-01
In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured P...
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
Sliding mode control-based linear functional observers for discrete-time stochastic systems
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.
Stochastic analysis of epidemics on adaptive time varying networks
Kotnis, Bhushan; Kuri, Joy
2013-06-01
Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an “adaptive threshold,” i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.
A one-time truncate and encode multiresolution stochastic framework
Energy Technology Data Exchange (ETDEWEB)
Abgrall, R.; Congedo, P.M.; Geraci, G., E-mail: gianluca.geraci@inria.fr
2014-01-15
In this work a novel adaptive strategy for stochastic problems, inspired from the classical Harten's framework, is presented. The proposed algorithm allows building, in a very general manner, stochastic numerical schemes starting from a whatever type of deterministic schemes and handling a large class of problems, from unsteady to discontinuous solutions. Its formulations permits to recover the same results concerning the interpolation theory of the classical multiresolution approach, but with an extension to uncertainty quantification problems. The present strategy permits to build numerical scheme with a higher accuracy with respect to other classical uncertainty quantification techniques, but with a strong reduction of the numerical cost and memory requirements. Moreover, the flexibility of the proposed approach allows to employ any kind of probability density function, even discontinuous and time varying, without introducing further complications in the algorithm. The advantages of the present strategy are demonstrated by performing several numerical problems where different forms of uncertainty distributions are taken into account, such as discontinuous and unsteady custom-defined probability density functions. In addition to algebraic and ordinary differential equations, numerical results for the challenging 1D Kraichnan–Orszag are reported in terms of accuracy and convergence. Finally, a two degree-of-freedom aeroelastic model for a subsonic case is presented. Though quite simple, the model allows recovering some physical key aspect, on the fluid/structure interaction, thanks to the quasi-steady aerodynamic approximation employed. The injection of an uncertainty is chosen in order to obtain a complete parameterization of the mass matrix. All the numerical results are compared with respect to classical Monte Carlo solution and with a non-intrusive Polynomial Chaos method.
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.
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.
The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process
Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko
2012-06-01
A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.
Suprathreshold stochastic resonance in neural processing tuned by correlation.
Durrant, Simon; Kang, Yanmei; Stocks, Nigel; Feng, Jianfeng
2011-07-01
Suprathreshold stochastic resonance (SSR) is examined in the context of integrate-and-fire neurons, with an emphasis on the role of correlation in the neuronal firing. We employed a model based on a network of spiking neurons which received synaptic inputs modeled by Poisson processes stimulated by a stepped input signal. The smoothed ensemble firing rate provided an output signal, and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons. It was found that an SSR effect was present in this context. We then examined a more biophysically plausible scenario where the noise was not controlled directly, but instead was tuned by the correlation between the inputs. The SSR effect remained present in this scenario with nonzero noise providing improved information transmission, and it was found that negative correlation between the inputs was optimal. Finally, an examination of SSR in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade-off between supratheshold and subthreshold components. We discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing.
Stochastic investigation of precipitation process for climatic variability identification
Sotiriadou, Alexia; Petsiou, Amalia; Feloni, Elisavet; Kastis, Paris; Iliopoulou, Theano; Markonis, Yannis; Tyralis, Hristos; Dimitriadis, Panayiotis; Koutsoyiannis, Demetris
2016-04-01
The precipitation process is important not only to hydrometeorology but also to renewable energy resources management. We use a dataset consisting of daily and hourly records around the globe to identify statistical variability with emphasis on the last period. Specifically, we investigate the occurrence of mean, maximum and minimum values and we estimate statistical properties such as marginal probability distribution function and the type of decay of the climacogram (i.e., mean process variance vs. scale). Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.
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.
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.
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.
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
QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION
Directory of Open Access Journals (Sweden)
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.
Stochastic calculus for fractional Brownian motion and related processes
Mishura, Yuliya S
2008-01-01
The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0
Kolmogorov's refined similarity hypotheses for turbulence and general stochastic processes
International Nuclear Information System (INIS)
Stolovitzky, G.; Sreenivasan, K.R.
1994-01-01
Kolmogorov's refined similarity hypotheses are shown to hold true for a variety of stochastic processes besides high-Reynolds-number turbulent flows, for which they were originally proposed. In particular, just as hypothesized for turbulence, there exists a variable V whose probability density function attains a universal form. Analytical expressions for the probability density function of V are obtained for Brownian motion as well as for the general case of fractional Brownian motion---the latter under some mild assumptions justified a posteriori. The properties of V for the case of antipersistent fractional Brownian motion with the Hurst exponent of 1/3 are similar in many details to those of high-Reynolds-number turbulence in atmospheric boundary layers a few meters above the ground. The one conspicuous difference between turbulence and the antipersistent fractional Brownian motion is that the latter does not possess the required skewness. Broad implications of these results are discussed
Identification of the structure parameters using short-time non-stationary stochastic excitation
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.
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
Analyzing a stochastic time series obeying a second-order differential equation.
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.
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.
SUPERPOSITION OF STOCHASTIC PROCESSES AND THE RESULTING PARTICLE DISTRIBUTIONS
International Nuclear Information System (INIS)
Schwadron, N. A.; Dayeh, M. A.; Desai, M.; Fahr, H.; Jokipii, J. R.; Lee, M. A.
2010-01-01
Many observations of suprathermal and energetic particles in the solar wind and the inner heliosheath show that distribution functions scale approximately with the inverse of particle speed (v) to the fifth power. Although there are exceptions to this behavior, there is a growing need to understand why this type of distribution function appears so frequently. This paper develops the concept that a superposition of exponential and Gaussian distributions with different characteristic speeds and temperatures show power-law tails. The particular type of distribution function, f ∝ v -5 , appears in a number of different ways: (1) a series of Poisson-like processes where entropy is maximized with the rates of individual processes inversely proportional to the characteristic exponential speed, (2) a series of Gaussian distributions where the entropy is maximized with the rates of individual processes inversely proportional to temperature and the density of individual Gaussian distributions proportional to temperature, and (3) a series of different diffusively accelerated energetic particle spectra with individual spectra derived from observations (1997-2002) of a multiplicity of different shocks. Thus, we develop a proof-of-concept for the superposition of stochastic processes that give rise to power-law distribution functions.
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.
The Ising Decision Maker: a binary stochastic network for choice response time.
Verdonck, Stijn; Tuerlinckx, Francis
2014-07-01
The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (c) 2014 APA, all rights reserved.
Stochastic behavior of a cold standby system with maximum repair time
Directory of Open Access Journals (Sweden)
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.
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
Profiles of the stochastic star formation process in spiral galaxies
International Nuclear Information System (INIS)
Comins, N.
1981-01-01
The formation of spiral arms in disc galaxies is generally attributed to the effects of spiral density waves. These relatively small (i.e. 5 per cent) non-axisymmetric perturbations of the interstellar medium cause spiral arms highlighted by O and B type stars to be created. In this paper another mechanism for spiral arm formation, the stochastic self-propagating star formation (SSPSF) process is examined. The SSPSF process combines the theory that shock waves from supernovae will compress the interstellar medium to create new stars, some of which will be massive enough to also supernova, with a disc galaxy's differential rotation to create spiral arms. The present work extends this process to the case where the probability of star formation from supernova shocks decreases with galactic radius. Where this work and previous investigations overlap (namely the uniform probability case), the agreement is very good, pretty spirals with various numbers of arms are generated. The decreasing probability cases, taken to vary as rsup(-j), still form spiral arms for 0 1.5 the spiral structure is essentially non-existent. (author)
Heterogeneous recurrence monitoring and control of nonlinear stochastic processes
Energy Technology Data Exchange (ETDEWEB)
Yang, Hui, E-mail: huiyang@usf.edu; Chen, Yun [Complex Systems Monitoring, Modeling and Analysis Laboratory, University of South Florida, Tampa, Florida 33620 (United States)
2014-03-15
Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.
Stochastic simulation of destruction processes in self-irradiated materials
Directory of Open Access Journals (Sweden)
T. Patsahan
2017-09-01
Full Text Available Self-irradiation damages resulting from fission processes are common phenomena observed in nuclear fuel containing (NFC materials. Numerous α-decays lead to local structure transformations in NFC materials. The damages appearing due to the impacts of heavy nuclear recoils in the subsurface layer can cause detachments of material particles. Such a behaviour is similar to sputtering processes observed during a bombardment of the material surface by a flux of energetic particles. However, in the NFC material, the impacts are initiated from the bulk. In this work we propose a two-dimensional mesoscopic model to perform a stochastic simulation of the destruction processes occurring in a subsurface region of NFC material. We describe the erosion of the material surface, the evolution of its roughness and predict the detachment of the material particles. Size distributions of the emitted particles are obtained in this study. The simulation results of the model are in a qualitative agreement with the size histogram of particles produced from the material containing lava-like fuel formed during the Chernobyl nuclear power plant disaster.
Modeling stochastic lead times in multi-echelon systems
Diks, E.B.; Heijden, van der M.C.
1996-01-01
In many multi-echelon inventory systems the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process which generates such lead times is usually not
Modeling stochastic lead times in multi-echelon systems
Diks, E.B.; van der Heijden, M.C.
1997-01-01
In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well
Structure and Randomness of Continuous-Time, Discrete-Event Processes
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.
Stochastic model of template-directed elongation processes in biology.
Schilstra, Maria J; Nehaniv, Chrystopher L
2010-10-01
We present a novel modular, stochastic model for biological template-based linear chain elongation processes. In this model, elongation complexes (ECs; DNA polymerase, RNA polymerase, or ribosomes associated with nascent chains) that span a finite number of template units step along the template, one after another, with semaphore constructs preventing overtaking. The central elongation module is readily extended with modules that represent initiation and termination processes. The model was used to explore the effect of EC span on motor velocity and dispersion, and the effect of initiation activator and repressor binding kinetics on the overall elongation dynamics. The results demonstrate that (1) motors that move smoothly are able to travel at a greater velocity and closer together than motors that move more erratically, and (2) the rate at which completed chains are released is proportional to the occupancy or vacancy of activator or repressor binding sites only when initiation or activator/repressor dissociation is slow in comparison with elongation. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.
Stochastic growth logistic model with aftereffect for batch fermentation process
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-06-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
Stochastic growth logistic model with aftereffect for batch fermentation process
International Nuclear Information System (INIS)
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-01-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits
Stochastic growth logistic model with aftereffect for batch fermentation process
Energy Technology Data Exchange (ETDEWEB)
Rosli, Norhayati; Ayoubi, Tawfiqullah [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah; Rahman, Haliza Abdul [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Salleh, Madihah Md [Department of Biotechnology Industry, Faculty of Biosciences and Bioengineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2014-06-19
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
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.
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...
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.
Optimal investment models with stochastic volatility: the time ...
African Journals Online (AJOL)
Therefore, a transform is primordial to express the value function in terms of a semilinear PDE with quadratic growth on the derivative term. Some proofs for the existence of smooth solution to this equation have been provided for this equation by Pham [11]. In that paper they illustrated some common stochastic volatility ...
Directory of Open Access Journals (Sweden)
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.
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.
Robustness Analysis of Hybrid Stochastic Neural Networks with Neutral Terms and Time-Varying Delays
Directory of Open Access Journals (Sweden)
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.
Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes
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.
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)
A stochastic fractional dynamics model of space-time variability of rain
Kundu, Prasun K.; Travis, James E.
2013-09-01
varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.
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.
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
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.
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.
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…
Kozachenko, Yuriy; Troshki, Viktor
2015-01-01
We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\\mathbb {T}),\\,p\\geq1$, is constructed.
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)
A comparison of the stochastic and machine learning approaches in hydrologic time series forecasting
Kim, T.; Joo, K.; Seo, J.; Heo, J. H.
2016-12-01
Hydrologic time series forecasting is an essential task in water resources management and it becomes more difficult due to the complexity of runoff process. Traditional stochastic models such as ARIMA family has been used as a standard approach in time series modeling and forecasting of hydrological variables. Due to the nonlinearity in hydrologic time series data, machine learning approaches has been studied with the advantage of discovering relevant features in a nonlinear relation among variables. This study aims to compare the predictability between the traditional stochastic model and the machine learning approach. Seasonal ARIMA model was used as the traditional time series model, and Random Forest model which consists of decision tree and ensemble method using multiple predictor approach was applied as the machine learning approach. In the application, monthly inflow data from 1986 to 2015 of Chungju dam in South Korea were used for modeling and forecasting. In order to evaluate the performances of the used models, one step ahead and multi-step ahead forecasting was applied. Root mean squared error and mean absolute error of two models were compared.
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays
Syed Ali, M.; Balasubramaniam, P.
2008-07-01
In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB.
Robust stability for uncertain stochastic fuzzy BAM neural networks with time-varying delays
International Nuclear Information System (INIS)
Syed Ali, M.; Balasubramaniam, P.
2008-01-01
In this Letter, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of uncertain stochastic fuzzy Bidirectional Associative Memory (BAM) neural networks with time-varying delays which are represented by the Takagi-Sugeno (TS) fuzzy models. A new class of uncertain stochastic fuzzy BAM neural networks with time varying delays has been studied and sufficient conditions have been derived to obtain conservative result in stochastic settings. The developed results are more general than those reported in the earlier literatures. In addition, the numerical examples are provided to illustrate the applicability of the result using LMI toolbox in MATLAB
StochPy: A Comprehensive, User-Friendly Tool for Simulating Stochastic Biological Processes
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
International Nuclear Information System (INIS)
Li Jianlong; Zeng Lingzao
2010-01-01
We discuss in detail the effects of the multi-time-delayed feedback driven by an aperiodic signal on the output of a stochastic resonance (SR) system. The effective potential function and dynamical probability density function (PDF) are derived. To measure the performance of the SR system in the presence of a binary random signal, the bit error rate (BER) defined by the dynamical PDF is employed, as is commonly used in digital communications. We find that the delay time, strength of the feedback, and number of time-delayed terms can change the effective potential function and the effective amplitude of the signal, and then affect the BER of the SR system. The numerical simulations strongly support the theoretical results. The goal of this investigation is to explore the effects of the multi-time-delayed feedback on SR and give a guidance to nonlinear systems in the application of information processing.
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.
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.
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...
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
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 stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator
González Ochoa, Héctor O.; Perales, Gualberto Solís; Epstein, Irving R.; Femat, Ricardo
2018-05-01
We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.
Incomplete Continuous-time Securities Markets with Stochastic Income Volatility
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
2014-01-01
We derive closed-form solutions for the equilibrium interest rate and market price of risk processes in an incomplete continuous-time market with uncertainty generated by Brownian motions. The economy has a finite number of heterogeneous exponential utility investors, who receive partially...
Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
In an incomplete continuous-time securities market governed by Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and equity premium processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income ...
Time to reach a given level of number of neutrons is stochastic analog of reactor period
International Nuclear Information System (INIS)
Ryazanov, V.V.
2012-01-01
In theory and in practice the operation of nuclear reactors to control the safety of the reactor is widely used deterministic value - the period of the reactor. It is proposed along with the period of the reactor using a stochastic analogue of this magnitude - a random amount of time to achieve a given level of a random process for the number of neutrons in the reactor. The paper discusses various features of the behavior of the mean and variance of time to achieve a specified level. This kind of features can be associated with impaired behavior of the reactor system. Introduced the value of time required to reach the level can be used to monitor and improve the safety of nuclear power plants
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.
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
H∞ state estimation of stochastic memristor-based neural networks with time-varying delays.
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.
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 processes analysis in nuclear reactor using ARMA models
International Nuclear Information System (INIS)
Zavaljevski, N.
1990-01-01
The analysis of ARMA model derived from general stochastic state equations of nuclear reactor is given. The dependence of ARMA model parameters on the main physical characteristics of RB nuclear reactor in Vinca is presented. Preliminary identification results are presented, observed discrepancies between theory and experiment are explained and the possibilities of identification improvement are anticipated. (author)
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus
2007-01-01
of stochastic origin can be observed in experiments. The models include a new approach to the platinum phase transition, which allows for a unification of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical behavior of the macroscopic reaction kinetics is investigated and shows good agreement...
Stochastic process variation in deep-submicron CMOS circuits and algorithms
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...
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.
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...
Learning process mapping heuristics under stochastic sampling overheads
Ieumwananonthachai, Arthur; Wah, Benjamin W.
1991-01-01
A statistical method was developed previously for improving process mapping heuristics. The method systematically explores the space of possible heuristics under a specified time constraint. Its goal is to get the best possible heuristics while trading between the solution quality of the process mapping heuristics and their execution time. The statistical selection method is extended to take into consideration the variations in the amount of time used to evaluate heuristics on a problem instance. The improvement in performance is presented using the more realistic assumption along with some methods that alleviate the additional complexity.
International Nuclear Information System (INIS)
Lee, Kwang Ho; Roh, Myung Sub
2013-01-01
There are so many different factors to consider when constructing a nuclear power plant successfully from planning to decommissioning. According to PMBOK, all projects have nine domains from a holistic project management perspective. They are equally important to all projects, however, this study focuses mostly on the processes required to manage timely completion of the project and conduct risk management. The overall objective of this study is to let you know what the risk analysis derived from scheduling of NPP project is, and understand how to implement the stochastic process modeling through risk management. Building the Nuclear Power Plant is required a great deal of time and fundamental knowledge related to all engineering. That means that integrated project scheduling management with so many activities is necessary and very important. Simulation techniques for scheduling of NPP project using Open Plan program, Crystal Ball program, and Minitab program can be useful tools for designing optimal schedule planning. Thus far, Open Plan and Monte Carlo programs have been used to calculate the critical path for scheduling network analysis. And also, Minitab program has been applied to monitor the scheduling risk. This approach to stochastic modeling through risk analysis of project activities is very useful for optimizing the schedules of activities using Critical Path Method and managing the scheduling control of NPP project. This study has shown new approach to optimal scheduling of NPP project, however, this does not consider the characteristic of activities according to the NPP site conditions. Hence, this study needs more research considering those factors
Energy Technology Data Exchange (ETDEWEB)
Lee, Kwang Ho; Roh, Myung Sub [KEPCO International Nuclear Graduate School, Ulsan (Korea, Republic of)
2013-10-15
There are so many different factors to consider when constructing a nuclear power plant successfully from planning to decommissioning. According to PMBOK, all projects have nine domains from a holistic project management perspective. They are equally important to all projects, however, this study focuses mostly on the processes required to manage timely completion of the project and conduct risk management. The overall objective of this study is to let you know what the risk analysis derived from scheduling of NPP project is, and understand how to implement the stochastic process modeling through risk management. Building the Nuclear Power Plant is required a great deal of time and fundamental knowledge related to all engineering. That means that integrated project scheduling management with so many activities is necessary and very important. Simulation techniques for scheduling of NPP project using Open Plan program, Crystal Ball program, and Minitab program can be useful tools for designing optimal schedule planning. Thus far, Open Plan and Monte Carlo programs have been used to calculate the critical path for scheduling network analysis. And also, Minitab program has been applied to monitor the scheduling risk. This approach to stochastic modeling through risk analysis of project activities is very useful for optimizing the schedules of activities using Critical Path Method and managing the scheduling control of NPP project. This study has shown new approach to optimal scheduling of NPP project, however, this does not consider the characteristic of activities according to the NPP site conditions. Hence, this study needs more research considering those factors.
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.
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
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
A stochastic space-time model for intermittent precipitation occurrences
Sun, Ying; Stein, Michael L.
2016-01-01
Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time t random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.
A stochastic space-time model for intermittent precipitation occurrences
Sun, Ying
2016-01-28
Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time t random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.
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
Transport properties of stochastic Lorentz models
Beijeren, H. van
Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed
Stochastic modeling of hourly rainfall times series in Campania (Italy)
Giorgio, M.; Greco, R.
2009-04-01
Occurrence of flowslides and floods in small catchments is uneasy to predict, since it is affected by a number of variables, such as mechanical and hydraulic soil properties, slope morphology, vegetation coverage, rainfall spatial and temporal variability. Consequently, landslide risk assessment procedures and early warning systems still rely on simple empirical models based on correlation between recorded rainfall data and observed landslides and/or river discharges. Effectiveness of such systems could be improved by reliable quantitative rainfall prediction, which can allow gaining larger lead-times. Analysis of on-site recorded rainfall height time series represents the most effective approach for a reliable prediction of local temporal evolution of rainfall. Hydrological time series analysis is a widely studied field in hydrology, often carried out by means of autoregressive models, such as AR, ARMA, ARX, ARMAX (e.g. Salas [1992]). Such models gave the best results when applied to the analysis of autocorrelated hydrological time series, like river flow or level time series. Conversely, they are not able to model the behaviour of intermittent time series, like point rainfall height series usually are, especially when recorded with short sampling time intervals. More useful for this issue are the so-called DRIP (Disaggregated Rectangular Intensity Pulse) and NSRP (Neymann-Scott Rectangular Pulse) model [Heneker et al., 2001; Cowpertwait et al., 2002], usually adopted to generate synthetic point rainfall series. In this paper, the DRIP model approach is adopted, in which the sequence of rain storms and dry intervals constituting the structure of rainfall time series is modeled as an alternating renewal process. Final aim of the study is to provide a useful tool to implement an early warning system for hydrogeological risk management. Model calibration has been carried out with hourly rainfall hieght data provided by the rain gauges of Campania Region civil
Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method.
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.
Producing a functional eukaryotic messenger RNA (mRNA) requires the coordinated activity of several large protein complexes to initiate transcription, elongate nascent transcripts, splice together exons, and cleave and polyadenylate the 3’ end. Kinetic competition between these various processes has been proposed to regulate mRNA maturation, but this model could lead to multiple, randomly determined, or stochastic, pathways or outcomes. Regulatory checkpoints have been suggested as a means of ensuring quality control. However, current methods have been unable to tease apart the contributions of these processes at a single gene or on a time scale that could provide mechanistic insight. To begin to investigate the kinetic relationship between transcription and splicing, Daniel Larson, Ph.D., of CCR’s Laboratory of Receptor Biology and Gene Expression, and his colleagues employed a single-molecule RNA imaging approach to monitor production and processing of a human β-globin reporter gene in living cells.
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.
Stochastic generation of hourly wind speed time series
International Nuclear Information System (INIS)
Shamshad, A.; Wan Mohd Ali Wan Hussin; Bawadi, M.A.; Mohd Sanusi, S.A.
2006-01-01
In the present study hourly wind speed data of Kuala Terengganu in Peninsular Malaysia are simulated by using transition matrix approach of Markovian process. The wind speed time series is divided into various states based on certain criteria. The next wind speed states are selected based on the previous states. The cumulative probability transition matrix has been formed in which each row ends with 1. Using the uniform random numbers between 0 and 1, a series of future states is generated. These states have been converted to the corresponding wind speed values using another uniform random number generator. The accuracy of the model has been determined by comparing the statistical characteristics such as average, standard deviation, root mean square error, probability density function and autocorrelation function of the generated data to those of the original data. The generated wind speed time series data is capable to preserve the wind speed characteristics of the observed data
Stochastic models in the DORIS position time series: estimates for IDS contribution to ITRF2014
Klos, Anna; Bogusz, Janusz; Moreaux, Guilhem
2017-11-01
This paper focuses on the investigation of the deterministic and stochastic parts of the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) weekly time series aligned to the newest release of ITRF2014. A set of 90 stations was divided into three groups depending on when the data were collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations and a stochastic part, all being estimated with maximum likelihood estimation. We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations. The quality of the most recent data has significantly improved. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. Among several tested models, the power-law process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from an autoregressive process to pure power-law noise with few stations characterised by a positive spectral index. For the latest observations, the medians of the velocity errors were equal to 0.3, 0.3 and 0.4 mm/year, respectively, for the North, East and Up components. In the best cases, a velocity uncertainty of DORIS sites of 0.1 mm/year is achievable when the appropriate coloured noise model is taken into consideration.
DEFF Research Database (Denmark)
Finlay, Chris; Olsen, Nils; Gillet, Nicolas
We present a new ensemble of time-dependent magnetic field models constructed from satellite and observatory data spanning 1997-2013 that are compatible with prior information concerning the temporal spectrum of core field variations. These models allow sharper field changes compared to tradition...... physical hypotheses can be tested by asking questions of the entire ensemble of core field models, rather than by interpreting any single model.......We present a new ensemble of time-dependent magnetic field models constructed from satellite and observatory data spanning 1997-2013 that are compatible with prior information concerning the temporal spectrum of core field variations. These models allow sharper field changes compared to traditional...... regularization methods based on minimizing the square of second or third time derivative. We invert satellite and observatory data directly by adopting the external field and crustal field modelling framework of the CHAOS model, but apply the stochastic process method of Gillet et al. (2013) to the core field...
A unified nonlinear stochastic time series analysis for climate science.
Moon, Woosok; Wettlaufer, John S
2017-03-13
Earth's orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.
Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.
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.
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 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...
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.
Relative entropy and waiting time for continuous-time Markov processes
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
Adaptive logical stochastic resonance in time-delayed synthetic genetic networks
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.
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus
2007-01-01
Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can......, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspondence with the successful description of experiments under low-pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena...
Effect of multiplicative noise on stationary stochastic process
Kargovsky, A. V.; Chikishev, A. Yu.; Chichigina, O. A.
2018-03-01
An open system that can be analyzed using the Langevin equation with multiplicative noise is considered. The stationary state of the system results from a balance of deterministic damping and random pumping simulated as noise with controlled periodicity. The dependence of statistical moments of the variable that characterizes the system on parameters of the problem is studied. A nontrivial decrease in the mean value of the main variable with an increase in noise stochasticity is revealed. Applications of the results in several physical, chemical, biological, and technical problems of natural and humanitarian sciences are discussed.
Stochastic Simulation and Forecast of Hydrologic Time Series Based on Probabilistic Chaos Expansion
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.
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...
Stochastic modeling of stock price process induced from the conjugate heat equation
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.
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.
Time processing in dyscalculia
Directory of Open Access Journals (Sweden)
marinella eCappelletti
2011-12-01
Full Text Available To test whether atypical number development may affect other types of quantity processing, we investigated temporal discrimination in adults with developmental dyscalculia (DD. This also allowed us to test whether (1 number and time may be sub-served by a common quantity system or decision mechanisms –in which case they may both be impaired, or (2 whether number and time are distinct –and therefore they may dissociate. Participants judged which of two successively presented horizontal lines was longer in duration, the first line being preceded by either a small or a large number prime (‘1’ or ‘9’ or by a neutral symbol (‘#’, or in third task decide which of two Arabic numbers (either ‘1’, ‘5’, ’9’ lasted longer. Results showed that (i DD’s temporal discriminability was normal as long as numbers were not part of the experimental design even as task-irrelevant stimuli; however (ii task-irrelevant numbers dramatically disrupted DD’s temporal discriminability, the more their salience increased, though the actual magnitude of the numbers had no effect; and in contrast (iii controls’ time perception was robust to the presence of numbers but modulated by numerical quantity such that small number primes or numerical stimuli made durations appear shorter than veridical and the opposite for larger numerical prime or numerical stimuli. This study is the first to investigate continuous quantity as time in a population with a congenital number impairment and to show that atypical development of numerical competence leaves continuous quantity processing spared. Our data support the idea of a partially shared quantity system across numerical and temporal dimensions, which allows dissociations and interactions among dimensions; furthermore, they suggest that impaired number in DD is unlikely to originate from systems initially dedicated to continuous quantity processing like time.
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
GCSRL - A Logic for Stochastic Reward Models with Timed and Untimed Behaviour
Kuntz, Matthias; Haverkort, Boudewijn R.; Cloth, L.
In this paper we define the logic GCSRL (generalised continuous stochastic reward logic) that provides means to reason about systems that have states which sojourn times are either greater zero, in which case this sojourn time is exponentially distributed (tangible states), or zero (vanishing
International Nuclear Information System (INIS)
Fu, Jin; Wu, Sheng; Li, Hong; Petzold, Linda R.
2014-01-01
The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy
Mashhoon, B.
1982-01-01
The influence of a stochastic and isotropic background of gravitational radiation on timing measurements of pulsars is investigated, and it is shown that pulsar timing noise may be used to establish a significant upper limit of about 10 to the -10th on the total energy density of very long-wavelength stochastic gravitational waves. This places restriction on the strength of very long wavelength gravitational waves in the Friedmann model, and such a background is expected to have no significant effect on the approximately 3 K electromagnetic background radiation or on the dynamics of a cluster of galaxies.
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.
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
Stochasticity, decoherence and an arrow of time from the ...
Indian Academy of Sciences (India)
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an arrow of time that follows from the fact that the replacement of the time derivative by the backward difference operator alone can preserve ...
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 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.
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.
Time processing in dyscalculia.
Cappelletti, Marinella; Freeman, Elliot D; Butterworth, Brian L
2011-01-01
To test whether atypical number development may affect other types of quantity processing, we investigated temporal discrimination in adults with developmental dyscalculia (DD). This also allowed us to test whether number and time may be sub-served by a common quantity system or decision mechanisms: if they do, both should be impaired in dyscalculia, but if number and time are distinct they should dissociate. Participants judged which of two successively presented horizontal lines was longer in duration, the first line being preceded by either a small or a large number prime ("1" or "9") or by a neutral symbol ("#"), or in a third task participants decided which of two Arabic numbers (either "1," "5," "9") lasted longer. Results showed that (i) DD's temporal discriminability was normal as long as numbers were not part of the experimental design, even as task-irrelevant stimuli; however (ii) task-irrelevant numbers dramatically disrupted DD's temporal discriminability the more their salience increased, though the actual magnitude of the numbers had no effect; in contrast (iii) controls' time perception was robust to the presence of numbers but modulated by numerical quantity: therefore small number primes or numerical stimuli seemed to make durations appear shorter than veridical, but longer for larger numerical prime or numerical stimuli. This study is the first to show spared temporal discrimination - a dimension of continuous quantity - in a population with a congenital number impairment. Our data reinforce the idea of a partially shared quantity system across numerical and temporal dimensions, which supports both dissociations and interactions among dimensions; however, they suggest that impaired number in DD is unlikely to originate from systems initially dedicated to continuous quantity processing like time.
Effect of the Potential Shape on the Stochastic Resonance Processes
Kenmoé, G. Djuidjé; Ngouongo, Y. J. Wadop; Kofané, T. C.
2015-10-01
The stochastic resonance (SR) induced by periodic signal and white noises in a periodic nonsinusoidal potential is investigated. This phenomenon is studied as a function of the friction coefficient as well as the shape of the potential. It is done through an investigation of the hysteresis loop area which is equivalent to the input energy lost by the system to the environment per period of the external force. SR is evident in some range of the shape parameter of the potential, but cannot be observed in the other range. Specially, variation of the shape potential affects significantly and not trivially the heigh of the potential barrier in the Kramers rate as well as the occurrence of SR. The finding results show crucial dependence of the temperature of occurrence of SR on the shape of the potential. It is noted that the maximum of the input energy generally decreases when the friction coefficient is increased.
Stochastic modeling and analysis of telecoms networks
Decreusefond, Laurent
2012-01-01
This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an
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.
Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality
Saldi, Naci; Yüksel, Serdar
2018-01-01
In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original mo...
Directory of Open Access Journals (Sweden)
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.
Stochastic skyline route planning under time-varying uncertainty
DEFF Research Database (Denmark)
Yang, Bin; Guo, Chenjuan; Jensen, Christian S.
2014-01-01
Different uses of a road network call for the consideration of different travel costs: in route planning, travel time and distance are typically considered, and green house gas (GHG) emissions are increasingly being considered. Further, travel costs such as travel time and GHG emissions are time...
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
Stochastic processes, multiscale modeling, and numerical methods for computational cellular biology
2017-01-01
This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of s...
Directory of Open Access Journals (Sweden)
Yajun Li
2015-01-01
Full Text Available This paper deals with the robust H∞ filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribed H∞ performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.
Effects of demographic stochasticity on biological community assembly on evolutionary time scales
Murase, Yohsuke
2010-04-13
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.
Effects of demographic stochasticity on biological community assembly on evolutionary time scales
Murase, Yohsuke; Shimada, Takashi; Ito, Nobuyasu; Rikvold, Per Arne
2010-01-01
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.
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.
A stochastic model of radiation carcinogenesis: Latent time distributions and their properties
International Nuclear Information System (INIS)
Klebanov, L.V.; Yakovlev, A.Yu.; Rachev, S.T.
1993-01-01
A stochastic model of radiation carcinogenesis is proposed that has much in common with the ideas suggested by M. Pike as early as 1966. The model allows one to obtain a parametric family of substochastic-type distributions for the time of tumor latency that provides a description of the rate of tumor development and the number of affected individuals. With this model it is possible to interpret data on tumor incidence in terms of promotion and progression processes. The basic model is developed for a prolonged irradiation at a constant dose rate and includes short-term irradiation as a special case. A limiting form of the latent time distribution for short-term irradiation at high doses is obtained. This distribution arises in the extreme value theory within the random minima framework. An estimate for the rate of convergence to a limiting distributions is given. Based on the proposed latent time distributions, long-term predictions of carcinogenic risk do not call for information about irradiation dose. As shown by computer simulation studies and real data analysis, the parametric estimation of carcinogenic risk appears to be robust to the loss of statistical information caused by the right-hand censoring of time-to-tumor observations. It seems likely that this property, although revealed by means of a purely empirical procedure, may be useful in selecting a model for the practical purpose of risk prediction. 44 refs., 3 figs., 1 tab
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
On the small time asymptotics of 3D stochastic primitive equations
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
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,
Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun
2015-12-01
This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.
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...
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...
ON THE ANISOTROPIC NORM OF DISCRETE TIME STOCHASTIC SYSTEMS WITH STATE DEPENDENT NOISE
Directory of Open Access Journals (Sweden)
Isaac Yaesh
2013-01-01
Full Text Available The purpose of this paper is to determine conditions for the bound-edness of the anisotropic norm of discrete-time linear stochastic sys-tems with state dependent noise. It is proved that these conditions canbe expressed in terms of the feasibility of a specific system of matrixinequalities.
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.
Directory of Open Access Journals (Sweden)
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.
A Family of Poisson Processes for Use in Stochastic Models of Precipitation
Penland, C.
2013-12-01
Both modified Poisson processes and compound Poisson processes can be relevant to stochastic parameterization of precipitation. This presentation compares the dynamical properties of these systems and discusses the physical situations in which each might be appropriate. If the parameters describing either class of systems originate in hydrodynamics, then proper consideration of stochastic calculus is required during numerical implementation of the parameterization. It is shown here that an improper numerical treatment can have severe implications for estimating rainfall distributions, particularly in the tails of the distributions and, thus, on the frequency of extreme events.
Continuous strong Markov processes in dimension one a stochastic calculus approach
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.
Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection
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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.
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.
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.
Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA.
Yang, Xian; Han, Rui; Guo, Yike; Bradley, Jeremy; Cox, Benita; Dickinson, Robert; Kitney, Richard
2012-01-01
Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of clinical pathway, thereby assisting
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
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.
Brownian motion and stochastic calculus
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...
Lopopolo, Alessandro; Frank, Stefan L; van den Bosch, Antal; Willems, Roel M
2017-01-01
Language comprehension involves the simultaneous processing of information at the phonological, syntactic, and lexical level. We track these three distinct streams of information in the brain by using stochastic measures derived from computational language models to detect neural correlates of phoneme, part-of-speech, and word processing in an fMRI experiment. Probabilistic language models have proven to be useful tools for studying how language is processed as a sequence of symbols unfolding in time. Conditional probabilities between sequences of words are at the basis of probabilistic measures such as surprisal and perplexity which have been successfully used as predictors of several behavioural and neural correlates of sentence processing. Here we computed perplexity from sequences of words and their parts of speech, and their phonemic transcriptions. Brain activity time-locked to each word is regressed on the three model-derived measures. We observe that the brain keeps track of the statistical structure of lexical, syntactic and phonological information in distinct areas.
Introduction to Stopping Time in Stochastic Finance Theory. Part II
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Jaeger Peter
2017-12-01
Full Text Available We start proceeding with the stopping time theory in discrete time with the help of the Mizar system [1], [4]. We prove, that the expression for two stopping times k1 and k2 not always implies a stopping time (k1 + k2 (see Theorem 6 in this paper. If you want to get a stopping time, you have to cut the function e.g. (k1 + k2 ⋂ T (see [2, p. 283 Remark 6.14]. Next we introduce the stopping time in continuous time. We are focused on the intervals [0, r] where r ∈ ℝ. We prove, that for I = [0, r] or I = [0,+∞[ the set {A ⋂ I : A ∈ Borel-Sets} is a σ-algebra of I (see Definition 6 in this paper, and more general given in [3, p.12 1.8e]. The interval I can be considered as a timeline from now to some point in the future. This set is necessary to define our next lemma. We prove the existence of the σ-algebra of the τ -past, where τ is a stopping time (see Definition 11 in this paper and [6, p.187, Definition 9.19]. If τ1 and τ2 are stopping times with τ1 is smaller or equal than τ2 we can prove, that the σ-algebra of the τ1-past is a subset of the σ-algebra of the τ2-past (see Theorem 9 in this paper and [6, p.187 Lemma 9.21]. Suppose, that you want to use Lemma 9.21 with some events, that never occur, see as a comparison the paper [5] and the example for ST(1={+∞} in the Summary. We don’t have the element +1 in our above-mentioned time intervals [0, r[ and [0,+1[. This is only possible if we construct a new σ-algebra on ℝ {−∞,+∞}. This construction is similar to the Borel-Sets and we call this σ-algebra extended Borel sets (see Definition 13 in this paper and [3, p. 21]. It can be proved, that {+∞} is an Element of extended Borel sets (see Theorem 21 in this paper. Now we use the interval [0,+∞] as a basis. We construct a σ-algebra on [0,+∞] similar to the book ([3, p. 12 18e], see Definition 18 in this paper, and call it extended Borel subsets. We prove for stopping times with this given σ-algebra, that
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.
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.
Stochastic Resonance and First Arrival Time for Excitable Systems
Duki, Solomon Fekade; Taye, Mesfin Asfaw
2018-06-01
We study the noise induced thermally activated barrier crossing of Brownian particles that hop in a piecewise linear potential. Using the exact analytic solutions and via numerical simulations not only we explore the dependence for the first passage time of a single particle but also we calculate the first arrival time for one particle out of N particles. The first arrival time decreases as the number of particles increases as expected. We then explore the thermally activated barrier crossing rate of the system in the presence of time varying signal. The dependence of signal to noise ratio SNR as well as the power amplification (η ) on model parameters is explored. η and SNR depict a pronounced peak at particular noise strength. In the presence of N particles, η is considerably amplified as N steps up showing the weak periodic signal plays a vital role in controlling the noise induced dynamics of the system. Moreover, for the sake of generality, the viscous friction γ is considered to decrease exponentially when the temperature T of the medium increases (γ =Be^{-A T}) as proposed originally by Reynolds (Philos Trans R Soc Lond 177:157, 1886).
A fire management simulation model using stochastic arrival times
Eric L. Smith
1987-01-01
Fire management simulation models are used to predict the impact of changes in the fire management program on fire outcomes. As with all models, the goal is to abstract reality without seriously distorting relationships between variables of interest. One important variable of fire organization performance is the length of time it takes to get suppression units to the...
Stochastic 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)
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
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.
Wang, Kang-Kang; Zong, De-Cai; Wang, Ya-Jun; Li, Sheng-Hong
2016-05-01
In this paper, the transition between the stable state of a big density and the extinction state and stochastic resonance (SR) for a time-delayed metapopulation system disturbed by colored cross-correlated noises are investigated. By applying the fast descent method, the small time-delay approximation and McNamara and Wiesenfeld's SR theory, we investigate the impacts of time-delay, the multiplicative, additive noises and colored cross-correlated noise on the SNR and the shift between the two states of the system. Numerical results show that the multiplicative, additive noises and time-delay can all speed up the transition from the stable state to the extinction state, while the correlation noise and its correlation time can slow down the extinction process of the population system. With respect to SNR, the multiplicative noise always weakens the SR effect, while noise correlation time plays a dual role in motivating the SR phenomenon. Meanwhile, time-delay mainly plays a negative role in stimulating the SR phenomenon. Conversely, it could motivate the SR effect to increase the strength of the cross-correlation noise in the SNR-β plot, while the increase of additive noise intensity will firstly excite SR, and then suppress the SR effect.
Moreno, Jackeline; Vogeley, Michael S.; Richards, Gordon; O'Brien, John T.; Kasliwal, Vishal
2018-01-01
We present rigorous testing of survey cadences (K2, SDSS, CRTS, & Pan-STARRS) for quasar variability science using a magnetohydrodynamics synthetic lightcurve and the canonical lightcurve from Kepler, Zw 229.15. We explain where the state of the art is in regards to physical interpretations of stochastic models (CARMA) applied to AGN variability. Quasar variability offers a time domain approach of probing accretion physics at the SMBH scale. Evidence shows that the strongest amplitude changes in the brightness of AGN occur on long timescales ranging from months to hundreds of days. These global behaviors can be constrained by survey data despite low sampling resolution. CARMA processes provide a flexible family of models used to interpolate between data points, predict future observations and describe behaviors in a lightcurve. This is accomplished by decomposing a signal into rise and decay timescales, frequencies for cyclic behavior and shock amplitudes. Characteristic timescales may point to length-scales over which a physical process operates such as turbulent eddies, warping or hotspots due to local thermal instabilities. We present the distribution of SDSS Stripe 82 quasars in CARMA parameters space that pass our cadence tests and also explain how the Damped Harmonic Oscillator model, CARMA(2,1), reduces to the Damped Random Walk, CARMA(1,0), given the data in a specific region of the parameter space.
Theory of time-averaged neutral dynamics with environmental stochasticity
Danino, Matan; Shnerb, Nadav M.
2018-04-01
Competition is the main driver of population dynamics, which shapes the genetic composition of populations and the assembly of ecological communities. Neutral models assume that all the individuals are equivalent and that the dynamics is governed by demographic (shot) noise, with a steady state species abundance distribution (SAD) that reflects a mutation-extinction equilibrium. Recently, many empirical and theoretical studies emphasized the importance of environmental variations that affect coherently the relative fitness of entire populations. Here we consider two generic time-averaged neutral models; in both the relative fitness of each species fluctuates independently in time but its mean is zero. The first (model A) describes a system with local competition and linear fitness dependence of the birth-death rates, while in the second (model B) the competition is global and the fitness dependence is nonlinear. Due to this nonlinearity, model B admits a noise-induced stabilization mechanism that facilitates the invasion of new mutants. A self-consistent mean-field approach is used to reduce the multispecies problem to two-species dynamics, and the large-N asymptotics of the emerging set of Fokker-Planck equations is presented and solved. Our analytic expressions are shown to fit the SADs obtained from extensive Monte Carlo simulations and from numerical solutions of the corresponding master equations.
Stochastic processes and functional analysis a volume of recent advances in honor of M. M. Rao
Krinik, Alan C
2004-01-01
This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes, as made manifest in M. M. Rao's prolific research achievements. Featuring a biography of M. M. Rao, a complete bibliography of his published works,
Goychuk, I
2001-08-01
Stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels. An exact expression for the information gain is obtained for the Poisson process with the signal-modulated spiking rate. This result allows one to generalize the conventional stochastic resonance (SR) problem (with periodic input signal) to the arbitrary signals of finite duration (nonstationary SR). Moreover, in the case of a periodic signal, the rate of information gain is compared with the conventional signal-to-noise ratio. The paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals.
Directory of Open Access Journals (Sweden)
Jing Cai
2016-01-01
Full Text Available Considering the wide application of condition-based maintenance in aeroengine maintenance practice, it becomes possible for aeroengines to carry out their preventive maintenance in just-in-time (JIT manner by reasonably planning their shop visits (SVs. In this study, an approach is proposed to make aeroengine SV decisions following the concept of JIT. Firstly, a state space model (SSM for aeroengine based on exhaust gas temperature margin is developed to predict the remaining useful life (RUL of aeroengine. Secondly, the effect of SV decisions on risk and service level (SL is analyzed, and an optimization of the aeroengine SV decisions based on RUL and stochastic repair time is performed to carry out JIT manner with the requirement of safety and SL. Finally, a case study considering two CFM-56 aeroengines is presented to demonstrate the proposed approach. The results show that predictive accuracy of RUL with SSM is higher than with linear regression, and the process of SV decisions is simple and feasible for airlines to improve the inventory management level of their aeroengines.
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....
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.
Strategy Complexity of Finite-Horizon Markov Decision Processes and Simple Stochastic Games
DEFF Research Database (Denmark)
Ibsen-Jensen, Rasmus; Chatterjee, Krishnendu
2012-01-01
Markov decision processes (MDPs) and simple stochastic games (SSGs) provide a rich mathematical framework to study many important problems related to probabilistic systems. MDPs and SSGs with finite-horizon objectives, where the goal is to maximize the probability to reach a target state in a given...
Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes
Cloth, L.; de Alfaro, L.; Gilmore, S.; Bohnenkamp, H.C.; Haverkort, Boudewijn R.H.M.
2001-01-01
In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an
Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks
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.
Reconstructing the hidden states in time course data of stochastic models.
Zimmer, Christoph
2015-11-01
Parameter estimation is central for analyzing models in Systems Biology. The relevance of stochastic modeling in the field is increasing. Therefore, the need for tailored parameter estimation techniques is increasing as well. Challenges for parameter estimation are partial observability, measurement noise, and the computational complexity arising from the dimension of the parameter space. This article extends the multiple shooting for stochastic systems' method, developed for inference in intrinsic stochastic systems. The treatment of extrinsic noise and the estimation of the unobserved states is improved, by taking into account the correlation between unobserved and observed species. This article demonstrates the power of the method on different scenarios of a Lotka-Volterra model, including cases in which the prey population dies out or explodes, and a Calcium oscillation system. Besides showing how the new extension improves the accuracy of the parameter estimates, this article analyzes the accuracy of the state estimates. In contrast to previous approaches, the new approach is well able to estimate states and parameters for all the scenarios. As it does not need stochastic simulations, it is of the same order of speed as conventional least squares parameter estimation methods with respect to computational time. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
Kinetic theory of age-structured stochastic birth-death processes
Greenman, Chris D.; Chou, Tom
2016-01-01
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.
DEFF Research Database (Denmark)
Foddai, Alessandro; Enøe, Claes; Krogh, Kaspar
2014-01-01
A stochastic simulation model was developed to estimate the time from introduction ofBovine Viral Diarrhea Virus (BVDV) in a herd to detection of antibodies in bulk tank milk(BTM) samples using three ELISAs. We assumed that antibodies could be detected, after afixed threshold prevalence of seroco......A stochastic simulation model was developed to estimate the time from introduction ofBovine Viral Diarrhea Virus (BVDV) in a herd to detection of antibodies in bulk tank milk(BTM) samples using three ELISAs. We assumed that antibodies could be detected, after afixed threshold prevalence......, which was the most efficient ELISA, could detect antibodiesin the BTM of a large herd 280 days (95% prediction interval: 218; 568) after a transientlyinfected (TI) milking cow has been introduced into the herd. The estimated time to detectionafter introduction of one PI calf was 111 days (44; 605...
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.
International Nuclear Information System (INIS)
Olsson, Magnus; Perninge, Magnus; Soeder, Lennart
2010-01-01
The inclusion of wind power into power systems has a significant impact on the demand for real-time balancing power due to the stochastic nature of wind power production. The overall aim of this paper is to present probabilistic models of the impact of large-scale integration of wind power on the continuous demand in MW for real-time balancing power. This is important not only for system operators, but also for producers and consumers since they in most systems through various market solutions provide balancing power. Since there can occur situations where the wind power variations cancel out other types of deviations in the system, models on an hourly basis are not sufficient. Therefore the developed model is in continuous time and is based on stochastic differential equations (SDE). The model can be used within an analytical framework or in Monte Carlo simulations. (author)
Stochastic Greybox Modeling for Control of an Alternating Activated Sludge Process
DEFF Research Database (Denmark)
Halvgaard, Rasmus Fogtmann; Vezzaro, Luca; Grum, M.
We present a stochastic greybox model of a BioDenitro WWTP that can be used for short time horizon Model Predictive Control. The model is based on a simpliﬁed ASM1 model and takes model uncertainty in to account. It estimates unmeasured state variables in the system, e.g. the inlet concentration...
Energy Technology Data Exchange (ETDEWEB)
Lutaif, N.A. [Departamento de Clínica Médica, Faculdade de Ciências Médicas, Universidade Estadual de Campinas, Campinas, SP (Brazil); Palazzo, R. Jr [Departamento de Telemática, Faculdade de Engenharia Elétrica e Computação, Universidade Estadual de Campinas, Campinas, SP (Brazil); Gontijo, J.A.R. [Departamento de Clínica Médica, Faculdade de Ciências Médicas, Universidade Estadual de Campinas, Campinas, SP (Brazil)
2014-01-17
Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile.
International Nuclear Information System (INIS)
Lutaif, N.A.; Palazzo, R. Jr; Gontijo, J.A.R.
2014-01-01
Maintenance of thermal homeostasis in rats fed a high-fat diet (HFD) is associated with changes in their thermal balance. The thermodynamic relationship between heat dissipation and energy storage is altered by the ingestion of high-energy diet content. Observation of thermal registers of core temperature behavior, in humans and rodents, permits identification of some characteristics of time series, such as autoreference and stationarity that fit adequately to a stochastic analysis. To identify this change, we used, for the first time, a stochastic autoregressive model, the concepts of which match those associated with physiological systems involved and applied in male HFD rats compared with their appropriate standard food intake age-matched male controls (n=7 per group). By analyzing a recorded temperature time series, we were able to identify when thermal homeostasis would be affected by a new diet. The autoregressive time series model (AR model) was used to predict the occurrence of thermal homeostasis, and this model proved to be very effective in distinguishing such a physiological disorder. Thus, we infer from the results of our study that maximum entropy distribution as a means for stochastic characterization of temperature time series registers may be established as an important and early tool to aid in the diagnosis and prevention of metabolic diseases due to their ability to detect small variations in thermal profile
Monte Carlo simulation of induction time and metastable zone width; stochastic or deterministic?
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.
An Innovative Real-time Environment for Unified Deterministic and Stochastic Groundwater Modeling
Li, S.; Liu, Q.
2003-12-01
Despite an exponential growth of computational capability over the last two decades-one that has allowed computational science and engineering to become a unique, powerful tool for scientific discovery-the extreme cost of groundwater modeling continues to limit its use. This occurs primarily because the modeling paradigm that has been employed for decades limits our ability to take full advantage of recent developments in computer, communication, graphic, and visualization technologies. In this presentation we introduce an innovative and sophisticated computational environment for groundwater modeling that promises to eliminate the current bottleneck and greatly expand the utility of computational tools for scientific discovery related to groundwater. Based on a set of efficient and robust computational algorithms, the new software system, called Interactive Groundwater (IGW), allows simulating complex flow and transport in aquifers subject to both systematic and "randomly" varying stresses and geological and chemical heterogeneity. Adopting a new paradigm, IGW eliminates a major bottleneck inherent in the traditional fragmented modeling technologies and enables real-time modeling, real-time visualization, real-time analysis, and real-time presentation. IGW functions as a "numerical laboratory" in which a researcher can freely explore in real-time: creating visually an aquifer of desired configurations, interactively imposing desired stresses, and then immediately investigating and visualizing the geology and the processes of flow and contaminant transport and transformation. A modeler can pause to edit at any time and interact on-line with any aspects (e.g., conceptual and numerical representation, boundary conditions, model solvers, and ways of visualization and analysis) of the integrated modeling process; he/she can initiate or stop, whenever needed, particle tracking, plume modeling, subscale modeling, cross-sectional modeling, stochastic modeling, monitoring
Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models
Zhang, Xin
2016-01-01
Asymptotic behavior of implied volatility is of our interest in this dissertation. For extreme strike, we consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the asset price density for large or smal...
Effects of time delay on stochastic resonance of the stock prices in financial system
International Nuclear Information System (INIS)
Li, Jiang-Cheng; Li, Chun; Mei, Dong-Cheng
2014-01-01
The effect of time delay on stochastic resonance of the stock prices in finance system was investigated. The time delay is introduced into the Heston model driven by the extrinsic and intrinsic periodic information for stock price. The signal power amplification (SPA) was calculated by numerical simulation. The results indicate that an optimal critical value of delay time maximally enhances the reverse-resonance in the behaviors of SPA as a function of long-run variance of volatility or cross correlation coefficient between noises for both cases of intrinsic and extrinsic periodic information. Moreover, in both cases, being a critical value in the delay time, when the delay time takes value below the critical value, reverse-resonance increases with the delay time increasing, however, when the delay time takes value above the critical value, the reverse-resonance decrease with the delay time increasing. - Highlights: • The effects of delay time on stochastic resonance of the stock prices was investigated. • There is an optimal critical value of delay time maximally enhances the reverse-resonance • The reverse-resonance increases with the delay time increasing as the delay time takes value below the critical value • The reverse-resonance decrease with the delay time increasing as the delay time takes value above the critical value
Effects of time delay on stochastic resonance of the stock prices in financial system
Energy Technology Data Exchange (ETDEWEB)
Li, Jiang-Cheng [Department of Physics, Yunnan University, Kunming, 650091 (China); Li, Chun [Department of Computer Science, Puer Teachers' College, Puer 665000 (China); Mei, Dong-Cheng, E-mail: meidch@ynu.edu.cn [Department of Physics, Yunnan University, Kunming, 650091 (China)
2014-06-13
The effect of time delay on stochastic resonance of the stock prices in finance system was investigated. The time delay is introduced into the Heston model driven by the extrinsic and intrinsic periodic information for stock price. The signal power amplification (SPA) was calculated by numerical simulation. The results indicate that an optimal critical value of delay time maximally enhances the reverse-resonance in the behaviors of SPA as a function of long-run variance of volatility or cross correlation coefficient between noises for both cases of intrinsic and extrinsic periodic information. Moreover, in both cases, being a critical value in the delay time, when the delay time takes value below the critical value, reverse-resonance increases with the delay time increasing, however, when the delay time takes value above the critical value, the reverse-resonance decrease with the delay time increasing. - Highlights: • The effects of delay time on stochastic resonance of the stock prices was investigated. • There is an optimal critical value of delay time maximally enhances the reverse-resonance • The reverse-resonance increases with the delay time increasing as the delay time takes value below the critical value • The reverse-resonance decrease with the delay time increasing as the delay time takes value above the critical value.
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.
Directory of Open Access Journals (Sweden)
Pengfei Guo
2014-01-01
Full Text Available This paper deals with the fault detection problem for a class of discrete-time wireless networked control systems described by switching topology with uncertainties and disturbances. System states of each individual node are affected not only by its own measurements, but also by other nodes’ measurements according to a certain network topology. As the topology of system can be switched in a stochastic way, we aim to design H∞ fault detection observers for nodes in the dynamic time-delay systems. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are acquired to guarantee the existence of the filters satisfying the H∞ performance constraint, and observer gains are derived by solving linear matrix inequalities. Finally, an illustrated example is provided to verify the effectiveness of the theoretical results.
Volatility Degree Forecasting of Stock Market by Stochastic Time Strength Neural Network
Directory of Open Access Journals (Sweden)
Haiyan Mo
2013-01-01
Full Text Available In view of the applications of artificial neural networks in economic and financial forecasting, a stochastic time strength function is introduced in the backpropagation neural network model to predict the fluctuations of stock price changes. In this model, stochastic time strength function gives a weight for each historical datum and makes the model have the effect of random movement, and then we investigate and forecast the behavior of volatility degrees of returns for the Chinese stock market indexes and some global market indexes. The empirical research is performed in testing the prediction effect of SSE, SZSE, HSI, DJIA, IXIC, and S&P 500 with different selected volatility degrees in the established model.
Robust stability for stochastic bidirectional associative memory neural networks with time delays
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.
An extension of clarke's model with stochastic amplitude flip processes
Hoel, Hakon; Nyberg, Henrik
2014-01-01
. 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
A note on "Multicriteria adaptive paths in stochastic, time-varying networks"
DEFF Research Database (Denmark)
Pretolani, Daniele; Nielsen, Lars Relund; Andersen, Kim Allan
In a recent paper, Opasanon and Miller-Hooks study multicriteria adaptive paths in stochastic time-varying networks. They propose a label correcting algorithm for finding the full set of efficient strategies. In this note we show that their algorithm is not correct, since it is based on a property...... that does not hold in general. Opasanon and Miller-Hooks also propose an algorithm for solving a parametric problem. We give a simplified algorithm which is linear in the input size....
Improved result on stability analysis of discrete stochastic neural networks with time delay
International Nuclear Information System (INIS)
Wu Zhengguang; Su Hongye; Chu Jian; Zhou Wuneng
2009-01-01
This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.
International Nuclear Information System (INIS)
Papiez, L.; Moskvin, V.; Tulovsky, V.
2001-01-01
The process of angular-spatial evolution of multiple scattering of charged particles can be described by a special case of Boltzmann integro-differential equation called Lewis equation. The underlying stochastic process for this evolution is the compound Poisson process on the surface of the unit sphere. The significant portion of events that constitute compound Poisson process that describes multiple scattering have diffusional character. This property allows to analyze the process of angular-spatial evolution of multiple scattering of charged particles as combination of soft and hard collision processes and compute appropriately its transition densities. These computations provide a method of the approximate solution to the Lewis equation. (orig.)
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
Modeling laser velocimeter signals as triply stochastic Poisson processes
Mayo, W. T., Jr.
1976-01-01
Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.
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
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.
Moeeni, Hamid; Bonakdari, Hossein; Fatemi, Seyed Ehsan
2017-04-01
Because time series stationarization has a key role in stochastic modeling results, three methods are analyzed in this study. The methods are seasonal differencing, seasonal standardization and spectral analysis to eliminate the periodic effect on time series stationarity. First, six time series including 4 streamflow series and 2 water temperature series are stationarized. The stochastic term for these series obtained with ARIMA is subsequently modeled. For the analysis, 9228 models are introduced. It is observed that seasonal standardization and spectral analysis eliminate the periodic term completely, while seasonal differencing maintains seasonal correlation structures. The obtained results indicate that all three methods present acceptable performance overall. However, model accuracy in monthly streamflow prediction is higher with seasonal differencing than with the other two methods. Another advantage of seasonal differencing over the other methods is that the monthly streamflow is never estimated as negative. Standardization is the best method for predicting monthly water temperature although it is quite similar to seasonal differencing, while spectral analysis performed the weakest in all cases. It is concluded that for each monthly seasonal series, seasonal differencing is the best stationarization method in terms of periodic effect elimination. Moreover, the monthly water temperature is predicted with more accuracy than monthly streamflow. The criteria of the average stochastic term divided by the amplitude of the periodic term obtained for monthly streamflow and monthly water temperature were 0.19 and 0.30, 0.21 and 0.13, and 0.07 and 0.04 respectively. As a result, the periodic term is more dominant than the stochastic term for water temperature in the monthly water temperature series compared to streamflow series.
Stochastic model of milk homogenization process using Markov's chain
Directory of Open Access Journals (Sweden)
A. A. Khvostov
2016-01-01
Full Text Available The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model parameters was carried out by minimizing the standard deviation calculated from the experimental data for each fraction of dairy products fat phase. As the set of experimental data processing results of the micrographic images of fat globules of whole milk samples distribution which were subjected to homogenization at different pressures were used. Pattern Search method was used as optimization method with the Latin Hypercube search algorithm from Global Optimization Тoolbox library. The accuracy of calculations averaged over all fractions of 0.88% (the relative share of units, the maximum relative error was 3.7% with the homogenization pressure of 30 MPa, which may be due to the very abrupt change in properties from the original milk in the particle size distribution at the beginning of the homogenization process and the lack of experimental data at homogenization pressures of below the specified value. The mathematical model proposed allows to calculate the profile of volume and mass distribution of the fat phase (fat globules in the product, depending on the homogenization pressure and can be used in the laboratory and research of dairy products composition, as well as in the calculation, design and modeling of the process equipment of the dairy industry enterprises.
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
CERN. Geneva; ANDERSON, Dustin James; DOGLIONI, Caterina
2015-01-01
The LHC provides experiments with an unprecedented amount of data. Experimental collaborations need to meet storage and computing requirements for the analysis of this data: this is often a limiting factor in the physics program that would be achievable if the whole dataset could be analysed. In this talk, I will describe the strategies adopted by the LHCb, CMS and ATLAS collaborations to overcome these limitations and make the most of LHC data: data parking, data scouting, and real-time analysis.
Mo Zhou; Joseph Buongiorno
2011-01-01
Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...
Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method
International Nuclear Information System (INIS)
Inoue, Jun-ichi
2010-01-01
In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range (d(= ∞)-dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding (d + 1)-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. In the steady state, we show that the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems and discuss several possible extensions of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we shall use our procedure to evaluate the decoding process of Bayesian image restoration. With the assistance of the concept of dynamical replica theory (the DRT), we derive the zero-temperature flow equation of image restoration measure showing some 'non-monotonic' behaviour in its time evolution.
Streeter, Lee
2017-07-01
Time-of-flight range imaging is analyzed using stochastic calculus. Through a series of interpretations and simplifications, the stochastic model leads to two methods for estimating linear radial velocity: maximum likelihood estimation on the transition probability distribution between measurements, and a new method based on analyzing the measured correlation waveform and its first derivative. The methods are tested in a simulated motion experiment from (-40)-(+40) m/s, with data from a camera imaging an object on a translation stage. In tests maximum likelihood is slow and unreliable, but when it works it estimates the linear velocity with standard deviation of 1 m/s or better. In comparison the new method is fast and reliable but works in a reduced velocity range of (-20)-(+20) m/s with standard deviation ranging from 3.5 m/s to 10 m/s.
Directory of Open Access Journals (Sweden)
Ryota Mori
2015-01-01
Full Text Available Airport congestion, in particular congestion of departure aircraft, has already been discussed by other researches. Most solutions, though, fail to account for uncertainties. Since it is difficult to remove uncertainties of the operations in the real world, a strategy should be developed assuming such uncertainties exist. Therefore, this research develops a fast-time stochastic simulation model used to validate various methods in order to decrease airport congestion level under existing uncertainties. The surface movement data is analyzed first, and the uncertainty level is obtained. Next, based on the result of data analysis, the stochastic simulation model is developed. The model is validated statistically and the characteristics of airport operation under existing uncertainties are investigated.
Stochastic behavior of cooling processes in hot nuclei
International Nuclear Information System (INIS)
de Oliveira, P.M.; Sa Martins, J.S.; Szanto de Toledo, A.
1997-01-01
The collapse of structure effects observed in hot nuclei is interpreted in terms of a dynamic lattice model which describes the process of nucleon (clusters) evaporation from a hot nucleus, predicting the final mass distribution. Results are compared with experimental data for the 10 B+ 9 Be and 10 B+ 10 B reactions, and indicate that the structures observed in the low-energy mass distributions in both simulation and experiment are a consequence of the competition between the residual interactions and the thermalization dissipative process. As a characteristic feature of complex evolving systems, this competition leads to long term memory during the dissipative path, the observables becoming thus insensitive to the actual microscopic interactions. copyright 1997 The American Physical Society
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Noble Mark
2006-05-01
Full Text Available Abstract Background The purpose of this paper is two-fold. The first objective is to validate the assumptions behind a stochastic model developed earlier by these authors to describe oligodendrocyte generation in cell culture. The second is to generate time-lapse data that may help biomathematicians to build stochastic models of cell proliferation and differentiation under other experimental scenarios. Results Using time-lapse video recording it is possible to follow the individual evolutions of different cells within each clone. This experimental technique is very laborious and cannot replace model-based quantitative inference from clonal data. However, it is unrivalled in validating the structure of a stochastic model intended to describe cell proliferation and differentiation at the clonal level. In this paper, such data are reported and analyzed for oligodendrocyte precursor cells cultured in vitro. Conclusion The results strongly support the validity of the most basic assumptions underpinning the previously proposed model of oligodendrocyte development in cell culture. However, there are some discrepancies; the most important is that the contribution of progenitor cell death to cell kinetics in this experimental system has been underestimated.
Stochastic processes in physics and chemistry. Revised and enlarged ed.
International Nuclear Information System (INIS)
Van Kampen, N.G.
1992-01-01
Three major changes have been made to this revised and updated edition. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated
Reflection Positive Stochastic Processes Indexed by Lie Groups
Jorgensen, Palle E. T.; Neeb, Karl-Hermann; Ólafsson, Gestur
2016-06-01
Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary representation of a symmetric Lie group to a unitary representation of its Cartan dual. In this article we continue our investigation of representation theoretic aspects of reflection positivity by discussing reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations.
Tempered stable distributions stochastic models for multiscale processes
Grabchak, Michael
2015-01-01
This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.
Reddy, V R; Reddy, T G; Reddy, P Y; Reddy, K R
2003-01-01
An AC modulation technique is described to convert stochastic signal variations into an amplitude variation and its retrieval through Fourier analysis. It is shown that this AC detection of signals of stochastic processes when processed through auto- and cross-correlation techniques improve the signal-to-noise ratio; the correlation techniques serve a similar purpose of frequency and phase filtering as that of phase-sensitive detection. A few model calculations applied to nuclear spectroscopy measurements such as Angular Correlations, Mossbauer spectroscopy and Pulse Height Analysis reveal considerable improvement in the sensitivity of signal detection. Experimental implementation of the technique is presented in terms of amplitude variations of harmonics representing the derivatives of normal spectra. Improved detection sensitivity to spectral variations is shown to be significant. These correlation techniques are general and can be made applicable to all the fields of particle counting where measurements ar...
Whole-field visual motion drives swimming in larval zebrafish via a stochastic process.
Portugues, Ruben; Haesemeyer, Martin; Blum, Mirella L; Engert, Florian
2015-05-01
Caudo-rostral whole-field visual motion elicits forward locomotion in many organisms, including larval zebrafish. Here, we investigate the dependence on the latency to initiate this forward swimming as a function of the speed of the visual motion. We show that latency is highly dependent on speed for slow speeds (1.5 s, which is much longer than neuronal transduction processes. What mechanisms underlie these long latencies? We propose two alternative, biologically inspired models that could account for this latency to initiate swimming: an integrate and fire model, which is history dependent, and a stochastic Poisson model, which has no history dependence. We use these models to predict the behavior of larvae when presented with whole-field motion of varying speed and find that the stochastic process shows better agreement with the experimental data. Finally, we discuss possible neuronal implementations of these models. © 2015. Published by The Company of Biologists Ltd.
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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.
International Nuclear Information System (INIS)
Colombino, A.; Mosiello, R.; Norelli, F.; Jorio, V.M.; Pacilio, N.
1975-01-01
A nuclear system kinetics is formulated according to a stochastic approach. The detailed probability balance equations are written for the probability of finding the mixed population of neutrons and detected neutrons, i.e. detectrons, at a given level for a given instant of time. Equations are integrated in search of a probability profile: a series of cases is analyzed through a progressive criterium. It tends to take into account an increasing number of physical processes within the chosen model. The most important contribution is that solutions interpret analytically experimental conditions of equilibrium (moise analysis) and non equilibrium (pulsed neutron measurements, source drop technique, start up procedures)
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.
Model-free stochastic processes studied with q-wavelet-based informational tools
International Nuclear Information System (INIS)
Perez, D.G.; Zunino, L.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.
2007-01-01
We undertake a model-free investigation of stochastic processes employing q-wavelet based quantifiers, that constitute a generalization of their Shannon counterparts. It is shown that (i) interesting physical information becomes accessible in such a way (ii) for special q values the quantifiers are more sensitive than the Shannon ones and (iii) there exist an implicit relationship between the Hurst parameter H and q within this wavelet framework
Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science
Li, Shilong; Yin, Chuancun; Zhao, Xia; Dai, Hongshuai
2017-01-01
Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigat...
Stochastic processes, optimization, and control theory a volume in honor of Suresh Sethi
Yan, Houmin
2006-01-01
This edited volume contains 16 research articles. It presents recent and pressing issues in stochastic processes, control theory, differential games, optimization, and their applications in finance, manufacturing, queueing networks, and climate control. One of the salient features is that the book is highly multi-disciplinary. The book is dedicated to Professor Suresh Sethi on the occasion of his 60th birthday, in view of his distinguished career.
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Akira Ikuta
2014-01-01
Full Text Available In real sound environment system, a specific signal shows various types of probability distribution, and the observation data are usually contaminated by external noise (e.g., background noise of non-Gaussian distribution type. Furthermore, there potentially exist various nonlinear correlations in addition to the linear correlation between input and output time series. Consequently, often the system input and output relationship in the real phenomenon cannot be represented by a simple model using only the linear correlation and lower order statistics. In this study, complex sound environment systems difficult to analyze by using usual structural method are considered. By introducing an estimation method of the system parameters reflecting correlation information for conditional probability distribution under existence of the external noise, a prediction method of output response probability for sound environment systems is theoretically proposed in a suitable form for the additive property of energy variable and the evaluation in decibel scale. The effectiveness of the proposed stochastic signal processing method is experimentally confirmed by applying it to the observed data in sound environment systems.
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.
Eichhorn, Ralf; Aurell, Erik
2014-04-01
theory for small deviations from equilibrium, in which a general framework is constructed from the analysis of non-equilibrium states close to equilibrium. In a next step, Prigogine and others developed linear irreversible thermodynamics, which establishes relations between transport coefficients and entropy production on a phenomenological level in terms of thermodynamic forces and fluxes. However, beyond the realm of linear response no general theoretical results were available for quite a long time. This situation has changed drastically over the last 20 years with the development of stochastic thermodynamics, revealing that the range of validity of thermodynamic statements can indeed be extended deep into the non-equilibrium regime. Early developments in that direction trace back to the observations of symmetry relations between the probabilities for entropy production and entropy annihilation in non-equilibrium steady states [5-8] (nowadays categorized in the class of so-called detailed fluctuation theorems), and the derivations of the Bochkov-Kuzovlev [9, 10] and Jarzynski relations [11] (which are now classified as so-called integral fluctuation theorems). Apart from its fundamental theoretical interest, the developments in stochastic thermodynamics have experienced an additional boost from the recent experimental progress in fabricating, manipulating, controlling and observing systems on the micro- and nano-scale. These advances are not only of formidable use for probing and monitoring biological processes on the cellular, sub-cellular and molecular level, but even include the realization of a microscopic thermodynamic heat engine [12] or the experimental verification of Landauer's principle in a colloidal system [13]. The scientific program Stochastic Thermodynamics held between 4 and 15 March 2013, and hosted by The Nordic Institute for Theoretical Physics (Nordita), was attended by more than 50 scientists from the Nordic countries and elsewhere, amongst them
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
International Nuclear Information System (INIS)
Vecherin, Sergey N; Ostashev, Vladimir E; Wilson, D Keith; Ziemann, A
2008-01-01
Time-dependent stochastic inversion (TDSI) was recently developed for acoustic travel-time tomography of the atmosphere. This type of tomography allows reconstruction of temperature and wind-velocity fields given the location of sound sources and receivers and the travel times between all source–receiver pairs. The quality of reconstruction provided by TDSI depends on the geometry of the transducer array. However, TDSI has not been studied for the geometry with reciprocal sound transmission. This paper is focused on three aspects of TDSI. First, the use of TDSI in reciprocal sound transmission arrays is studied in numerical and physical experiments. Second, efficiency of time-dependent and ordinary stochastic inversion (SI) algorithms is studied in numerical experiments. Third, a new model of noise in the input data for TDSI is developed that accounts for systematic errors in transducer positions. It is shown that (i) a separation of the travel times into temperature and wind-velocity components in tomography with reciprocal transmission does not improve the reconstruction, (ii) TDSI yields a better reconstruction than SI and (iii) the developed model of noise yields an accurate reconstruction of turbulent fields and estimation of errors in the reconstruction
A stochastic post-processing method for solar irradiance forecasts derived from NWPs models
Lara-Fanego, V.; Pozo-Vazquez, D.; Ruiz-Arias, J. A.; Santos-Alamillos, F. J.; Tovar-Pescador, J.
2010-09-01
Solar irradiance forecast is an important area of research for the future of the solar-based renewable energy systems. Numerical Weather Prediction models (NWPs) have proved to be a valuable tool for solar irradiance forecasting with lead time up to a few days. Nevertheless, these models show low skill in forecasting the solar irradiance under cloudy conditions. Additionally, climatic (averaged over seasons) aerosol loading are usually considered in these models, leading to considerable errors for the Direct Normal Irradiance (DNI) forecasts during high aerosols load conditions. In this work we propose a post-processing method for the Global Irradiance (GHI) and DNI forecasts derived from NWPs. Particularly, the methods is based on the use of Autoregressive Moving Average with External Explanatory Variables (ARMAX) stochastic models. These models are applied to the residuals of the NWPs forecasts and uses as external variables the measured cloud fraction and aerosol loading of the day previous to the forecast. The method is evaluated for a set one-moth length three-days-ahead forecast of the GHI and DNI, obtained based on the WRF mesoscale atmospheric model, for several locations in Andalusia (Southern Spain). The Cloud fraction is derived from MSG satellite estimates and the aerosol loading from the MODIS platform estimates. Both sources of information are readily available at the time of the forecast. Results showed a considerable improvement of the forecasting skill of the WRF model using the proposed post-processing method. Particularly, relative improvement (in terms of the RMSE) for the DNI during summer is about 20%. A similar value is obtained for the GHI during the winter.
Power Laws in Stochastic Processes for Social Phenomena: An Introductory Review
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.
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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.
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.
Dimension reduction of Karhunen-Loeve expansion for simulation of stochastic processes
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.
Energy Technology Data Exchange (ETDEWEB)
Chorošajev, Vladimir [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania); Gelzinis, Andrius; Valkunas, Leonas [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania); Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Sauletekio 3, 10222 Vilnius (Lithuania); Abramavicius, Darius, E-mail: darius.abramavicius@ff.vu.lt [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania)
2016-12-20
Highlights: • The Davydov ansatze can be used for finite temperature simulations with an extension. • The accuracy is high if the system is strongly coupled to the environmental phonons. • The approach can simulate time-resolved fluorescence spectra. - Abstract: Time dependent variational approach is a convenient method to characterize the excitation dynamics in molecular aggregates for different strengths of system-bath interaction a, which does not require any additional perturbative schemes. Until recently, however, this method was only applicable in zero temperature case. It has become possible to extend this method for finite temperatures with the introduction of stochastic time dependent variational approach. Here we present a comparison between this approach and the exact hierarchical equations of motion approach for describing excitation dynamics in a broad range of temperatures. We calculate electronic population evolution, absorption and auxiliary time resolved fluorescence spectra in different regimes and find that the stochastic approach shows excellent agreement with the exact approach when the system-bath coupling is sufficiently large and temperatures are high. The differences between the two methods are larger, when temperatures are lower or the system-bath coupling is small.
Extinction time of a stochastic predator-prey model by the generalized cell mapping method
Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao
2018-03-01
The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.
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.
Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson
2017-02-01
Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a
Deriving Link Travel-Time Distributions via Stochastic Speed Processes
2004-02-01
general, an exact expression for the inverse transform is available when Equation (9) is a vector of rational functions in both of the complex variables...Otherwise, recovery of the original function is accom- plished through the inverse transform f t= 1 2(j ∫ c+j c−j estf ∗s ds (13) which is usually...given by f x t = f ∗s1 s2 = ∫ 0 ∫ 0 e−s1x+s2tf x t dx dt (14) with inverse transform f x t = 1 4(2 ∫ c1+j c1−j ∫ c2+j c2−j e
International Nuclear Information System (INIS)
Zhang Min-Min; Mei Dong-Cheng; Wang Can-Jun
2011-01-01
The effects of the time delay on the upper bound of the time derivative of information entropy are investigated in a time-delayed dynamical system driven by correlated noise. Using the Markov approximation of the stochastic delay differential equations and the Schwartz inequality principle, we obtain an analytical expression for the upper bound U B (t) of the time derivative of the information entropy. The results show that there is a critical value of τ (delay time), and U B (t) presents opposite behaviours on difference sides of the critical value. For the case of the weak additive noise, τ can induce a reentrance transition. Delay time τ also causes a reversal behaviour in U B (t)-λ plot, where λ denotes the degree of the correlation between the two noises. (general)
Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation
Directory of Open Access Journals (Sweden)
Wantao Jia
2018-02-01
Full Text Available We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental randomness is modeled as Poisson white noise. The stochastic averaging method and the perturbation method are applied to calculate the approximate stationary probability density functions for both predator and prey populations. The influences of system parameters and the Poisson white noises are investigated in detail based on the approximate stationary probability density functions. It is found that, increasing time delay parameter as well as the mean arrival rate and the variance of the amplitude of the Poisson white noise will enhance the fluctuations of the prey and predator population. While the larger value of self-competition parameter will reduce the fluctuation of the system. Furthermore, the results from Monte Carlo simulation are also obtained to show the effectiveness of the results from averaging method.
On a stochastic process associated to non-abelian gauge fields
International Nuclear Information System (INIS)
Vilela Mendes, R.
1989-01-01
A stochastic process is constructed from a ground state measure that generalizes to non-abelian fields the ground state of abelian (free) gauge fields without fermions. Using a latticized version one shows how the process leads to a well-defined quantum theory in the Schroedinger representation. An analysis of the qualitative behaviour of the theory seems to imply a quasi-free behaviour at short distances and a maximally disordered field strength configuration for the low-momentum component of the ground state. Scaling relations for the mass gap are inferred from the theory of small random perturbations of dynamical systems. (orig.)
SDE decomposition and A-type stochastic interpretation in nonequilibrium processes
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.
Liu, Hongjian; Wang, Zidong; Shen, Bo; Huang, Tingwen; Alsaadi, Fuad E
2018-06-01
This paper is concerned with the globally exponential stability problem for a class of discrete-time stochastic memristive neural networks (DSMNNs) with both leakage delays as well as probabilistic time-varying delays. For the probabilistic delays, a sequence of Bernoulli distributed random variables is utilized to determine within which intervals the time-varying delays fall at certain time instant. The sector-bounded activation function is considered in the addressed DSMNN. By taking into account the state-dependent characteristics of the network parameters and choosing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are established under which the underlying DSMNN is globally exponentially stable in the mean square. The derived conditions are made dependent on both the leakage and the probabilistic delays, and are therefore less conservative than the traditional delay-independent criteria. A simulation example is given to show the effectiveness of the proposed stability criterion. Copyright © 2018 Elsevier Ltd. All rights reserved.
Peccati, Giovanni
2016-01-01
Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolvi...
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)
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Directory of Open Access Journals (Sweden)
Yingwei Li
2014-01-01
Full Text Available The exponential synchronization issue for stochastic neural networks (SNNs with mixed time delays and Markovian jump parameters using sampled-data controller is investigated. Based on a novel Lyapunov-Krasovskii functional, stochastic analysis theory, and linear matrix inequality (LMI approach, we derived some novel sufficient conditions that guarantee that the master systems exponentially synchronize with the slave systems. The design method of the desired sampled-data controller is also proposed. To reflect the most dynamical behaviors of the system, both Markovian jump parameters and stochastic disturbance are considered, where stochastic disturbances are given in the form of a Brownian motion. The results obtained in this paper are a little conservative comparing the previous results in the literature. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.
Stochastic modeling for time series InSAR: with emphasis on atmospheric effects
Cao, Yunmeng; Li, Zhiwei; Wei, Jianchao; Hu, Jun; Duan, Meng; Feng, Guangcai
2018-02-01
Despite the many applications of time series interferometric synthetic aperture radar (TS-InSAR) techniques in geophysical problems, error analysis and assessment have been largely overlooked. Tropospheric propagation error is still the dominant error source of InSAR observations. However, the spatiotemporal variation of atmospheric effects is seldom considered in the present standard TS-InSAR techniques, such as persistent scatterer interferometry and small baseline subset interferometry. The failure to consider the stochastic properties of atmospheric effects not only affects the accuracy of the estimators, but also makes it difficult to assess the uncertainty of the final geophysical results. To address this issue, this paper proposes a network-based variance-covariance estimation method to model the spatiotemporal variation of tropospheric signals, and to estimate the temporal variance-covariance matrix of TS-InSAR observations. The constructed stochastic model is then incorporated into the TS-InSAR estimators both for parameters (e.g., deformation velocity, topography residual) estimation and uncertainty assessment. It is an incremental and positive improvement to the traditional weighted least squares methods to solve the multitemporal InSAR time series. The performance of the proposed method is validated by using both simulated and real datasets.
Quantum learning of classical stochastic processes: The completely positive realization problem
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
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
Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Bennett, Matthew R; Josić, Krešimir; Ott, William
2014-05-28
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.
Energy Technology Data Exchange (ETDEWEB)
Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Bennett, Matthew R. [Department of Biochemistry and Cell Biology, Rice University, Houston, Texas 77204, USA and Institute of Biosciences and Bioengineering, Rice University, Houston, Texas 77005 (United States); Josić, Krešimir [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Department of Biology and Biochemistry, University of Houston, Houston, Texas 77204 (United States)
2014-05-28
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.
International Nuclear Information System (INIS)
Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William; Bennett, Matthew R.; Josić, Krešimir
2014-01-01
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay
Robust stability analysis of uncertain stochastic neural networks with interval time-varying delay
International Nuclear Information System (INIS)
Feng Wei; Yang, Simon X.; Fu Wei; Wu Haixia
2009-01-01
This paper addresses the stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded, and the delay factor is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. A sufficient condition is derived such that for all admissible uncertainties, the considered neural network is robustly, globally, asymptotically stable in the mean square. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be effectively solved by some standard numerical packages. Finally, numerical examples are provided to demonstrate the usefulness of the proposed criteria.
Liu, Xiaomei; Li, Shengtao; Zhang, Kanjian
2017-08-01
In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation, we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology.
Stochastic modeling of catalytic processes in nanoporous materials: Beyond mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Garcia, Andres [Iowa State Univ., Ames, IA (United States)
2017-08-05
Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems can be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use
International Nuclear Information System (INIS)
Zwingelstein, Gilles; Thabet, Gabriel.
1977-01-01
Control algorithms for components of nuclear power plants are currently based on external diagnostic methods. Modeling and identification techniques for autoregressive moving average models (ARMA) for stochastic processes are described. The identified models provide a means of estimating the power spectral density with improved accuracy and computer time compared with the classical methods. They are particularly will suited for on-line estimation of the power spectral density. The observable stochastic process y (t) is modeled assuming that it is the output of a linear filter driven by Gaussian while noise w (t). Two identification schemes were tested to find the orders m and n of the ARMA (m,n) models and to estimate the parameters of the recursion equation relating the input and output signals. The first scheme consists in transforming the ARMA model to an autoregressive model. The parameters of this AR model are obtained using least squares estimation techniques. The second scheme consists in finding the parameters of the ARMA by nonlinear programming techniques. The power spectral density of y(t) is instantaneously deduced from these ARMA models [fr
Stochastic Processes and Queueing Theory used in Cloud Computer Performance Simulations
Directory of Open Access Journals (Sweden)
Florin-Catalin ENACHE
2015-10-01
Full Text Available The growing character of the cloud business has manifested exponentially in the last 5 years. The capacity managers need to concentrate on a practical way to simulate the random demands a cloud infrastructure could face, even if there are not too many mathematical tools to simulate such demands.This paper presents an introduction into the most important stochastic processes and queueing theory concepts used for modeling computer performance. Moreover, it shows the cases where such concepts are applicable and when not, using clear programming examples on how to simulate a queue, and how to use and validate a simulation, when there are no mathematical concepts to back it up.
International Nuclear Information System (INIS)
Vignes, J.
1986-01-01
Any result of algorithms provided by a computer always contains an error resulting from floating-point arithmetic round-off error propagation. Furthermore signal processing algorithms are also generally performed with data containing errors. The permutation-perturbation method, also known under the name CESTAC (controle et estimation stochastique d'arrondi de calcul) is a very efficient practical method for evaluating these errors and consequently for estimating the exact significant decimal figures of any result of algorithms performed on a computer. The stochastic approach of this method, its probabilistic proof, and the perfect agreement between the theoretical and practical aspects are described in this paper [fr
An approach to the drone fleet survivability assessment based on a stochastic continues-time model
Kharchenko, Vyacheslav; Fesenko, Herman; Doukas, Nikos
2017-09-01
An approach and the algorithm to the drone fleet survivability assessment based on a stochastic continues-time model are proposed. The input data are the number of the drones, the drone fleet redundancy coefficient, the drone stability and restoration rate, the limit deviation from the norms of the drone fleet recovery, the drone fleet operational availability coefficient, the probability of the drone failure-free operation, time needed for performing the required tasks by the drone fleet. The ways for improving the recoverable drone fleet survivability taking into account amazing factors of system accident are suggested. Dependencies of the drone fleet survivability rate both on the drone stability and the number of the drones are analysed.
Supply Chain Model with Stochastic Lead Time, Trade-Credit Financing, and Transportation Discounts
Directory of Open Access Journals (Sweden)
Sung Jun Kim
2017-01-01
Full Text Available This model extends a two-echelon supply chain model by considering the trade-credit policy, transportations discount to make a coordination mechanism between transportation discounts, trade-credit financing, number of shipments, quality improvement of products, and reduced setup cost in such a way that the total cost of the whole system can be reduced, where the supplier offers trade-credit-period to the buyer. For buyer, the backorder rate is considered as variable. There are two investments to reduce setup cost and to improve quality of products. The model assumes lead time-dependent backorder rate, where the lead time is stochastic in nature. By using the trade-credit policy, the model gives how the credit-period would be determined to achieve the win-win outcome. An iterative algorithm is designed to obtain the global optimum results. Numerical example and sensitivity analysis are given to illustrate the model.
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.
Analysis methods of stochastic transient electro–magnetic processes in electric traction system
Directory of Open Access Journals (Sweden)
T. M. Mishchenko
2013-04-01
Full Text Available Purpose. The essence and basic characteristics of calculation methods of transient electromagnetic processes in the elements and devices of non–linear dynamic electric traction systems taking into account the stochastic changes of voltages and currents in traction networks of power supply subsystem and power circuits of electric rolling stock are developed. Methodology. Classical methods and the methods of non–linear electric engineering, as well as probability theory method, especially the methods of stationary ergodic and non–stationary stochastic processes application are used in the research. Findings. Using the above-mentioned methods an equivalent circuit and the system of nonlinear integra–differential equations for electromagnetic condition of the double–track inter-substation zone of alternating current electric traction system are drawn up. Calculations allow obtaining electric traction current distribution in the areas of feeder zones. Originality. First of all the paper is interesting and important from scientific point of view due to the methods, which allow taking into account probabilistic character of change for traction voltages and electric traction system currents. On the second hand the researches develop the most efficient methods of nonlinear circuits’ analysis. Practical value. The practical value of the research is presented in application of the methods to the analysis of electromagnetic and electric energy processes in the traction power supply system in the case of high-speed train traffic.
Directory of Open Access Journals (Sweden)
Shilong Li
2018-03-01
Full Text Available In this paper, we introduce a class of stochastic interest model driven by a compoundPoisson process and a Brownian motion, in which the jumping times of force of interest obeyscompound Poisson process and the continuous tiny fluctuations are described by Brownian motion, andthe adjustment in each jump of interest force is assumed to be random. Based on the proposed interestmodel, we discuss the expected discounted function, the validity of the model and actuarial presentvalues of life annuities and life insurances under different parameters and distribution settings. Ournumerical results show actuarial values could be sensitive to the parameters and distribution settings,which shows the importance of introducing this kind interest model.
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
The Long Time Behavior of a Stochastic Logistic Model with Infinite Delay and Impulsive Perturbation
Lu, Chun; Wu, Kaining
2016-01-01
This paper considers a stochastic logistic model with infinite delay and impulsive perturbation. Firstly, with the space $C_{g}$ as phase space, the definition of solution to a stochastic functional differential equation with infinite delay and impulsive perturbation is established. According to this definition, we show that our model has an unique global positive solution. Then we establish the sufficient and necessary conditions for extinction and stochastic permanence of the...
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.
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.
Sun, Ying; Ding, Derui; Zhang, Sunjie; Wei, Guoliang; Liu, Hongjian
2018-07-01
In this paper, the non-fragile ?-? control problem is investigated for a class of discrete-time stochastic nonlinear systems under event-triggered communication protocols, which determine whether the measurement output should be transmitted to the controller or not. The main purpose of the addressed problem is to design an event-based output feedback controller subject to gain variations guaranteeing the prescribed disturbance attenuation level described by the ?-? performance index. By utilizing the Lyapunov stability theory combined with S-procedure, a sufficient condition is established to guarantee both the exponential mean-square stability and the ?-? performance for the closed-loop system. In addition, with the help of the orthogonal decomposition, the desired controller parameter is obtained in terms of the solution to certain linear matrix inequalities. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed event-based controller design scheme.
Discrete-time state estimation for stochastic polynomial systems over polynomial observations
Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.
2018-07-01
This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.
Energy Technology Data Exchange (ETDEWEB)
Dong, Jing [ORNL; Mahmassani, Hani S. [Northwestern University, Evanston
2011-01-01
This paper proposes a methodology to produce random flow breakdown endogenously in a mesoscopic operational model, by capturing breakdown probability and duration. Based on previous research findings that probability of flow breakdown can be represented as a function of flow rate and the duration can be characterized by a hazard model. By generating random flow breakdown at various levels and capturing the traffic characteristics at the onset of the breakdown, the stochastic network simulation model provides a tool for evaluating travel time variability. The proposed model can be used for (1) providing reliability related traveler information; (2) designing ITS (intelligent transportation systems) strategies to improve reliability; and (3) evaluating reliability-related performance measures of the system.
Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems
Mahdi Alavi, S. M.; Saif, Mehrdad
2013-12-01
This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.
The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory
DEFF Research Database (Denmark)
Govindan, Kannan
2015-01-01
A Vendor Managed Inventory (VMI) partnership places the responsibility on the vendor (rather than on buyers) to schedule purchase orders for inventory replenishment in the supply chain system. In this research, the supply chain network considers the Silver-Meal heuristic with an augmentation...... quantity replenishment policy between both traditional and VMI systems. We consider time-varying stochastic demand in two-echelon (one vendor, multiple retailers) supply chains. This paper seeks to find the supply chain that minimizes system cost through comparing performance between traditional and VMI...... systems. A mathematical model is developed, and total supply chain cost is used as the measure of comparison. The models are applied in both traditional and VMI supply chains based on pharmaceutical industry data, and we focus on total cost difference compared through the use of Adjusted Silver-Meal (ASM...
International Nuclear Information System (INIS)
Yan-Mei, Kang; Yao-Lin, Jiang
2008-01-01
To explore the influence of anomalous diffusion on stochastic resonance (SR) more deeply and effectively, the method of moments is extended to subdiffusive overdamped bistable fractional Fokker-Planck systems for calculating the long-time linear dynamic response. It is found that the method of moments attains high accuracy with the truncation order N = 10, and in normal diffusion such obtained spectral amplification factor (SAF) of the first-order harmonic is also confirmed by stochastic simulation. Observing the SAF of the odd-order harmonics we find some interesting results, i.e. for smaller driving frequency the decrease of sub diffusion exponent inhibits the stochastic resonance (SR), while for larger driving frequency the decrease of sub diffusion exponent enhances the second SR peak, but the first one vanishes and a double SR is induced in the third-order harmonic at the same time. These observations suggest that the anomalous diffusion has important influence on the bistable dynamics
International Nuclear Information System (INIS)
Miniati, Francesco
2015-01-01
We use the Matryoshka run to study the time-dependent statistics of structure-formation-driven turbulence in the intracluster medium of a 10 15 M ☉ galaxy cluster. We investigate the turbulent cascade in the inner megaparsec for both compressional and incompressible velocity components. The flow maintains approximate conditions of fully developed turbulence, with departures thereof settling in about an eddy-turnover time. Turbulent velocity dispersion remains above 700 km s –1 even at low mass accretion rate, with the fraction of compressional energy between 10% and 40%. The normalization and the slope of the compressional turbulence are susceptible to large variations on short timescales, unlike the incompressible counterpart. A major merger occurs around redshift z ≅ 0 and is accompanied by a long period of enhanced turbulence, ascribed to temporal clustering of mass accretion related to spatial clustering of matter. We test models of stochastic acceleration by compressional modes for the origin of diffuse radio emission in galaxy clusters. The turbulence simulation model constrains an important unknown of this complex problem and brings forth its dependence on the elusive microphysics of the intracluster plasma. In particular, the specifics of the plasma collisionality and the dissipation physics of weak shocks affect the cascade of compressional modes with strong impact on the acceleration rates. In this context radio halos emerge as complex phenomena in which a hierarchy of processes acting on progressively smaller scales are at work. Stochastic acceleration by compressional modes implies statistical correlation of radio power and spectral index with merging cores distance, both testable in principle with radio surveys
A stochastic analysis approach on the cost-time profile for selecting the best future state MA
Directory of Open Access Journals (Sweden)
Seyedhosseini, Seyed Mohammad
2015-05-01
Full Text Available In the literature on value stream mapping (VSM, the only basis for choosing the best future state map (FSM among the proposed alternatives is the time factor. As a result, the FSM is selected as the best option because it has the least amount of total production lead time (TPLT. In this paper, the cost factor is considered in the FSM selection process, in addition to the time factor. Thus, for each of the proposed FSMs, the cost-time profile (CTP is used. Two factors that are of particular importance for the customer and the manufacturer – the TPLT and the direct cost of the product – are reviewed and analysed by calculating the sub-area of the CTP curve, called the cost-time investment (CTI. In addition, variability in the generated data has been studied in each of the CTPs in order to choose the best FSM more precisely and accurately. Based on a proposed step-by-step stochastic analysis method, and also by using non-parametric Kernel estimation methods for estimating the probability density function of CTIs, the process of choosing the best FSM has been carried out, based not only on the minimum expected CTI, but also on the minimum expected variability amount in CTIs among proposed alternatives. By implementing this method during the process of choosing the best FSM, the manufacturing organisations will consider both the cost factor and the variability in the generated data, in addition to the time factor. Accordingly, the decision-making process proceeds more easily and logically than do traditional methods. Finally, to describe the effectiveness and applicability of the proposed method in this paper, it is applied to a case study on an industrial parts manufacturing company in Iran.
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)
Monitoring and pollution control: A stochastic process approach to model oil spills
International Nuclear Information System (INIS)
Viladrich-Grau, M.
1991-01-01
The first chapter analyzes the behavior of a firm in an environment with pollution externalities and technological progress. It is assumed that firms may not purposely violate the pollution control regulations but nonetheless, generate some pollution due to negligence. The model allows firms two possible actions: either increase the level of treated waste or pay an expected penalty if illegal pollution is detected. The results of the first chapter show that in a world with pollution externalities, technological progress does not guarantee increases in the welfare level. The second chapter models the occurrence of an oil spill as a stochastic event. The stochastic model developed allows one to see how each step of the spilling process is affected by each policy measure and to compare the relative efficiency of different measures in reducing spills. The third chapter estimates the parameters that govern oil spill frequency and size distribution. The author models how these parameters depend on two pollution prevention measures: monitoring of transfer operations and assessment of penalties. He shows that these measures reduce the frequency of oil spills
First-Passage-Time Distribution for Variable-Diffusion Processes
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.
Sulis, William H
2017-10-01
Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.
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)
Stochastic approaches for time series forecasting of boron: a case study of Western Turkey.
Durdu, Omer Faruk
2010-10-01
In the present study, a seasonal and non-seasonal prediction of boron concentrations time series data for the period of 1996-2004 from Büyük Menderes river in western Turkey are addressed by means of linear stochastic models. The methodology presented here is to develop adequate linear stochastic models known as autoregressive integrated moving average (ARIMA) and multiplicative seasonal autoregressive integrated moving average (SARIMA) to predict boron content in the Büyük Menderes catchment. Initially, the Box-Whisker plots and Kendall's tau test are used to identify the trends during the study period. The measurements locations do not show significant overall trend in boron concentrations, though marginal increasing and decreasing trends are observed for certain periods at some locations. ARIMA modeling approach involves the following three steps: model identification, parameter estimation, and diagnostic checking. In the model identification step, considering the autocorrelation function (ACF) and partial autocorrelation function (PACF) results of boron data series, different ARIMA models are identified. The model gives the minimum Akaike information criterion (AIC) is selected as the best-fit model. The parameter estimation step indicates that the estimated model parameters are significantly different from zero. The diagnostic check step is applied to the residuals of the selected ARIMA models and the results indicate that the residuals are independent, normally distributed, and homoscadastic. For the model validation purposes, the predicted results using the best ARIMA models are compared to the observed data. The predicted data show reasonably good agreement with the actual data. The comparison of the mean and variance of 3-year (2002-2004) observed data vs predicted data from the selected best models show that the boron model from ARIMA modeling approaches could be used in a safe manner since the predicted values from these models preserve the basic
Cotter, C J; Gottwald, G A; Holm, D D
2017-09-01
In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.