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Author : Björn Palmgren
Publisher :
ISBN 13 : 9789171461537
Total Pages : 116 pages
Book Rating : 4.4/5 (615 download)
Download or read book Limit Theorems for the Range of Markov Chains written by Björn Palmgren and published by . This book was released on 1981 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dmitry Dolgopyat
Publisher : Springer Nature
ISBN 13 : 3031326016
Total Pages : 348 pages
Book Rating : 4.0/5 (313 download)
Download or read book Local Limit Theorems for Inhomogeneous Markov Chains written by Dmitry Dolgopyat and published by Springer Nature. This book was released on 2023-07-31 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
Author : Hubert Hennion
Publisher : Springer
ISBN 13 : 3540446230
Total Pages : 150 pages
Book Rating : 4.5/5 (44 download)
Download or read book Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness written by Hubert Hennion and published by Springer. This book was released on 2003-07-01 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The usefulness of from the of techniques perturbation theory operators, to kernel for limit theorems for a applied quasi-compact positive Q, obtaining Markov chains for stochastic of or dynamical by describing properties systems, of Perron- Frobenius has been demonstrated in several All use a operator, papers. these works share the features the features that must be same specific general ; used in each stem from the nature of the functional particular case precise space where the of is and from the number of quasi-compactness Q proved eigenvalues of of modulus 1. We here a functional framework for Q give general analytical this method and we the aforementioned behaviour within it. It asymptotic prove is worth that this framework is to allow the unified noticing sufficiently general treatment of all the cases considered in the literature the previously specific ; characters of model translate into the verification of of simple hypotheses every a functional nature. When to Markov kernels or to Perr- applied Lipschitz Frobenius associated with these statements rise operators expanding give maps, to new results and the of known The main clarify proofs already properties. of the deals with a Markov kernel for which 1 is a part quasi-compact Q paper of modulus 1. An essential but is not the simple eigenvalue unique eigenvalue element of the work is the of the of peripheral Q precise description spectrums and of its To conclude the the results obtained perturbations.
Author : Alexei Kulik
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110458934
Total Pages : 268 pages
Book Rating : 4.1/5 (14 download)
Download or read book Ergodic Behavior of Markov Processes written by Alexei Kulik and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-20 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems
Author : Xia Chen
Publisher : American Mathematical Soc.
ISBN 13 : 082181060X
Total Pages : 225 pages
Book Rating : 4.8/5 (218 download)
Download or read book Limit Theorems for Functionals of Ergodic Markov Chains with General State Space written by Xia Chen and published by American Mathematical Soc.. This book was released on 1999 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working probability theory and statistics.
Author : Shlomo Levental
Publisher :
ISBN 13 :
Total Pages : 210 pages
Book Rating : 4.:/5 (89 download)
Download or read book Uniform Limit Theorems for Markov Chains written by Shlomo Levental and published by . This book was released on 1986 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Steven Orey
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.:/5 (319 download)
Download or read book Lecture Notes on Limit Theorems for Markov Chain Transition Probability Functions written by Steven Orey and published by . This book was released on 1968 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hubert Hennion
Publisher :
ISBN 13 : 9783662205389
Total Pages : 162 pages
Book Rating : 4.2/5 (53 download)
Download or read book Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness written by Hubert Hennion and published by . This book was released on 2014-01-15 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Steven Orey
Publisher :
ISBN 13 :
Total Pages : 126 pages
Book Rating : 4.3/5 (91 download)
Download or read book Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities written by Steven Orey and published by . This book was released on 1971 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sidney C. Port
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.E/5 ( download)
Download or read book Limit Theorems Involving Capacities for Recurrent Markov Chains written by Sidney C. Port and published by . This book was released on 1965 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic behavior of the quantity E(n) = The summation over all x of M(x) P sub x (V
Author : Kulik, Alexei
Publisher : Universitätsverlag Potsdam
ISBN 13 : 3869563389
Total Pages : 138 pages
Book Rating : 4.8/5 (695 download)
Download or read book Introduction to Ergodic rates for Markov chains and processes written by Kulik, Alexei and published by Universitätsverlag Potsdam. This book was released on 2015-10-20 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lecture notes aim for an introduction to the ergodic behaviour of Markov Processes and addresses graduate students, post-graduate students and interested readers. Different tools and methods for the study of upper bounds on uniform and weak ergodic rates of Markov Processes are introduced. These techniques are then applied to study limit theorems for functionals of Markov processes. This lecture course originates in two mini courses held at University of Potsdam, Technical University of Berlin and Humboldt University in spring 2013 and Ritsumameikan University in summer 2013. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.
Author : George Yin
Publisher : Springer Science & Business Media
ISBN 13 : 9780387219486
Total Pages : 372 pages
Book Rating : 4.2/5 (194 download)
Download or read book Discrete-Time Markov Chains written by George Yin and published by Springer Science & Business Media. This book was released on 2005 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on discrete-time-scale Markov chains, the contents of this book are an outgrowth of some of the authors' recent research. The motivation stems from existing and emerging applications in optimization and control of complex hybrid Markovian systems in manufacturing, wireless communication, and financial engineering. Much effort in this book is devoted to designing system models arising from these applications, analyzing them via analytic and probabilistic techniques, and developing feasible computational algorithms so as to reduce the inherent complexity. This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems. One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering. This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques. Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.
Author : Sidney C. Port
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (712 download)
Download or read book Ratio Limit Theorems for Markov Chains written by Sidney C. Port and published by . This book was released on 1964 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an irreducible, recurrent, Markov chain, with integer states, let N sub n(A) be the occupation time of A sy time n, where A is a finite set of states. The principal concern in this memorandum was to investigate various 'ratio limit theorems' for P sub x(N sub n(A) =k). Criteria were given for various ratio limits to exist. The limits (when they exist) were shown to be expressible in terms of an integral over the set of integers E completed with its dual recurrent boundary B. Applications were given to several specific Markov chains. (Author).
Author : Randal Douc
Publisher : Springer
ISBN 13 : 3319977040
Total Pages : 758 pages
Book Rating : 4.3/5 (199 download)
Download or read book Markov Chains written by Randal Douc and published by Springer. This book was released on 2018-12-11 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required). Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.
Author : Stephen Robert Kimbleton
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.:/5 (519 download)
Download or read book Stable Limit Theorems for Markov Chains written by Stephen Robert Kimbleton and published by . This book was released on 1967 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Burton Herbert Singer
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.F/5 ( download)
Download or read book Some Limit Theorems for Markov Chains and Related Occupancy Problems written by Burton Herbert Singer and published by . This book was released on 1967 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : G. George Yin
Publisher : Springer Science & Business Media
ISBN 13 : 1461443466
Total Pages : 442 pages
Book Rating : 4.4/5 (614 download)
Download or read book Continuous-Time Markov Chains and Applications written by G. George Yin and published by Springer Science & Business Media. This book was released on 2012-11-14 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.
