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On The Weak Convergence Of A Sequence Of General Stochastic Difference Equations To A Diffusion
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Book Synopsis Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory by : Harold Joseph Kushner
Download or read book Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory written by Harold Joseph Kushner and published by MIT Press. This book was released on 1984 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Mathematics of the USSR. written by and published by . This book was released on 1984 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Diffusion Approximation of a Sequence of Semimartingales and Its Application in Exploring the Asymptotic Behaviour of Some Queueing Networks by : Yi-Ju Chao
Download or read book Diffusion Approximation of a Sequence of Semimartingales and Its Application in Exploring the Asymptotic Behaviour of Some Queueing Networks written by Yi-Ju Chao and published by . This book was released on 1999 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Analysis by : M. T. Barlow
Download or read book Stochastic Analysis written by M. T. Barlow and published by Cambridge University Press. This book was released on 1991-10-25 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from the Symposium on stochastic analysis, which took place at the University of Durham in July 1990.
Book Synopsis Government Reports Announcements & Index by :
Download or read book Government Reports Announcements & Index written by and published by . This book was released on 1986 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probability Theory and Mathematical Statistics by : K. Ito
Download or read book Probability Theory and Mathematical Statistics written by K. Ito and published by Springer. This book was released on 2006-11-15 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems by : Harold Kushner
Download or read book Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).
Book Synopsis Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems by : Omar Anza Hafsa
Download or read book Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems written by Omar Anza Hafsa and published by World Scientific. This book was released on 2022-06-21 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.
Book Synopsis Journal of Mathematical Sciences, the University of Tokyo by :
Download or read book Journal of Mathematical Sciences, the University of Tokyo written by and published by . This book was released on 2005 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete-Time Approximations and Limit Theorems by : Yuliya Mishura
Download or read book Discrete-Time Approximations and Limit Theorems written by Yuliya Mishura and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-10-25 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The De Gruyter Series in Probability and Stochastics is devoted to the publication of high-level monographs and specialized graduate texts in any branch of modern probability theory and stochastics, along with their numerous applications in other parts of mathematics, physics and informatics, in economics and finance, and in the life sciences. The aim of the series is to present recent research results in the form of authoritative and comprehensive works that will serve the probability and stochastics community as basis for further research. Editorial Board Itai Benjamini, Weizmann Institute of Science, Israel Jean Bertoin, Universität Zürich, Switzerland Michel Ledoux, Université de Toulouse, France René L. Schilling, Technische Universität Dresden, Germany
Book Synopsis Stochastic Differential Equations and Diffusion Processes by : N. Ikeda
Download or read book Stochastic Differential Equations and Diffusion Processes written by N. Ikeda and published by Elsevier. This book was released on 2014-06-28 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.
Book Synopsis Recent Advances in Statistics by : M. Haseeb Rizvi
Download or read book Recent Advances in Statistics written by M. Haseeb Rizvi and published by Academic Press. This book was released on 2014-05-10 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday is a collection of papers on statistics in honor of Herman Chernoff on the occasion of his 60th birthday. Topics covered range from sequential analysis (including designs) to optimization (including control theory), nonparametrics (including large sample theory), and statistical graphics. Comprised of 27 chapters, this book begins with a discussion on optimal stopping of Brownian motion, followed by an analysis of sequential design of comparative clinical trials. A two-sample sequential test for shift with one sample size fixed in advance is then presented. Subsequent chapters focus on set-valued parameters and set-valued statistics; large deviations of the maximum likelihood estimate in the Markov chain case; the limiting behavior of multiple roots of the likelihood equation; and optimal uniform rate of convergence for nonparametric estimators of a density function and its derivatives. The book concludes by considering significance and confidence levels, closed regions and models, and discrete distributions. This monograph should be of interest to students, researchers, and specialists in the fields of mathematics and statistics.
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 1228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hiroshima Mathematical Journal written by and published by . This book was released on 1984-05 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
