Local Limit Theorems For Inhomogeneous Markov Chains

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Local Limit Theorems For Inhomogeneous Markov Chains

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Author : Dmitry Dolgopyat
language : en
Publisher: Springer Nature
Release Date : 2023-07-31

Local Limit Theorems For Inhomogeneous Markov Chains written by Dmitry Dolgopyat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.

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.

Coin Turning Random Walks And Inhomogeneous Markov Chains

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Author : Janos Englander
language : en
Publisher: World Scientific
Release Date : 2024-11-22

Coin Turning Random Walks And Inhomogeneous Markov Chains written by Janos Englander and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-22 with Mathematics categories.

This research monograph explores new frontiers in Markov chains. Although time-homogeneous Markov chains are well understood, this is not at all the case with time-inhomogeneous ones. The book, after a review on the classical theory of homogeneous chains, including the electrical network approach, introduces several new models which involve inhomogeneous chains as well as related new types of random walks (for example, 'coin turning', 'conservative' and 'Rademacher' walk). Scaling limits, the breakdown of the classical limit theorems as well as recurrence and transience are investigated. The relationship with urn models is the subject of two chapters, providing additional connections to other parts of probability theory.Random walks on random graphs are discussed as well, as an area where the method of electric networks is especially useful. This is illustrated by presenting random walks in random environments and random labyrinths.The monograph puts emphasis on showing examples and open problems besides providing rigorous analysis of the models.Several figures illustrate the main ideas, and a large number of exercises challenge the interested reader.

Journal Of Research Of The National Bureau Of Standards

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Author : United States. National Bureau of Standards
language : en
Publisher:
Release Date : 1963

Journal Of Research Of The National Bureau Of Standards written by United States. National Bureau of Standards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Mathematical physics categories.

Finite Markov Processes And Their Applications

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Author : Marius Iosifescu
language : en
Publisher: Courier Corporation
Release Date : 2007-06-05

Finite Markov Processes And Their Applications written by Marius Iosifescu and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-05 with Mathematics categories.

Self-contained treatment covers both theory and applications. Topics include the fundamental role of homogeneous infinite Markov chains in the mathematical modeling of psychology and genetics. 1980 edition.

Recent Soviet Contributions To Mathematics

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Author : Joseph P. LaSalle
language : en
Publisher:
Release Date : 1962

Recent Soviet Contributions To Mathematics written by Joseph P. LaSalle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Mathematicians categories.

Compound Renewal Processes

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Author : A. A. Borovkov
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-30

Compound Renewal Processes written by A. A. Borovkov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-30 with Mathematics categories.

Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.

Technical Abstract Bulletin

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Author : Defense Documentation Center (U.S.)
language : en
Publisher:
Release Date : 1964

Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Military art and science categories.

U S Government Research Reports

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Author :
language : en
Publisher:
Release Date : 1964

U S Government Research Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Science categories.

Twenty Four Papers On Statistics And Probability

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :

Twenty Four Papers On Statistics And Probability written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Moscow University Mathematics Bulletin

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Author : Московский государственный университет им. М.В. Ломоносова
language : en
Publisher:
Release Date : 1981

Moscow University Mathematics Bulletin written by Московский государственный университет им. М.В. Ломоносова and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.