Convergence Of Stochastic Processes
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Convergence Of Stochastic Processes
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Author : D. Pollard
language : en
Publisher: David Pollard
Release Date : 1984-10-08
Convergence Of Stochastic Processes written by D. Pollard and has been published by David Pollard this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-10-08 with Mathematics categories.
Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.
Weak Convergence Of Stochastic Processes
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Author : Vidyadhar S. Mandrekar
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-09-26
Weak Convergence Of Stochastic Processes written by Vidyadhar S. Mandrekar and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.
The purpose of this book is to present results on the subject of weak convergence in function spaces to study invariance principles in statistical applications to dependent random variables, U-statistics, censor data analysis. Different techniques, formerly available only in a broad range of literature, are for the first time presented here in a self-contained fashion. Contents: Weak convergence of stochastic processes Weak convergence in metric spaces Weak convergence on C[0, 1] and D[0,∞) Central limit theorem for semi-martingales and applications Central limit theorems for dependent random variables Empirical process Bibliography
Limit Theorems For Stochastic Processes
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Author : Jean Jacod
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Limit Theorems For Stochastic Processes written by Jean Jacod and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.
Convergence Of Stochastic Processes
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Author : D. Pollard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Convergence Of Stochastic Processes written by D. Pollard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions. The material is somewhat arbitrarily divided into results used to prove consistency theorems and results used to prove central limit theorems. This has allowed me to put the easier material in Chapter II, with the hope of enticing the casual reader to delve deeper. Chapters III through VI deal with more classical material, as seen from a different perspective. The novelties are: convergence for measures that don't live on borel a-fields; the joys of working with the uniform metric on D[O, IJ; and finite-dimensional approximation as the unifying idea behind weak convergence. Uniform tightness reappears in disguise as a condition that justifies the finite-dimensional approximation. Only later is it exploited as a method for proving the existence of limit distributions. The last chapter has a heuristic flavor. I didn't want to confuse the martingale issues with the martingale facts.
Weak Convergence Methods And Singularly Perturbed Stochastic Control And Filtering Problems
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Author : Harold Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Weak Convergence Methods And Singularly Perturbed Stochastic Control And Filtering Problems written by Harold Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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).
Stochastic Process Limits
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Author : Ward Whitt
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-08
Stochastic Process Limits written by Ward Whitt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-08 with Mathematics categories.
From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews
Empirical Processes With Applications To Statistics
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Author : Galen R. Shorack
language : en
Publisher: SIAM
Release Date : 2009-09-24
Empirical Processes With Applications To Statistics written by Galen R. Shorack and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-24 with Mathematics categories.
Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables. It also includes applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods, and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition.
Convergence Of Stochastic Processes
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Author : David Pollard
language : en
Publisher:
Release Date : 1984-01-01
Convergence Of Stochastic Processes written by David Pollard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Convergence categories.
Stochastic Convergence
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Author : Eugene Lukacs
language : en
Publisher: Academic Press
Release Date : 2014-07-03
Stochastic Convergence written by Eugene Lukacs and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Mathematics categories.
Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the power series whose coefficients are random variables, the stochastic integrals and derivatives, and the characteristics of the normal distribution of infinite sums of random variables. The last chapter discusses the characterization of the Wiener process and of stable processes. This book will prove useful to mathematicians and advance mathematics students.
Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory
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Author : Harold Joseph Kushner
language : en
Publisher: MIT Press
Release Date : 1984
Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory written by Harold Joseph Kushner and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Computers categories.
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.