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Local limit theorems for inhomogeneo...

Dolgopyat, Dmitry.

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Local limit theorems for inhomogeneous Markov chains

Record Type:	Electronic resources : Monograph/item
Title/Author:	Local limit theorems for inhomogeneous Markov chains/ by Dmitry Dolgopyat, Omri M. Sarig.
Author:	Dolgopyat, Dmitry.
other author:	Sarig, Omri M.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xiii, 342 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Limit theorems (Probability theory) -
Online resource:	https://doi.org/10.1007/978-3-031-32601-1
ISBN:	9783031326011

Local limit theorems for inhomogeneous Markov chains
Dolgopyat, Dmitry.

Local limit theorems for inhomogeneous Markov chains[electronic resource] /by Dmitry Dolgopyat, Omri M. Sarig. - Cham :Springer International Publishing :2023. - xiii, 342 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23311617-9692 ;. - Lecture notes in mathematics ;v. 2331..

This book extends the local central limit theorem to inhomogeneous 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. It 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 numerous examples, a comprehensive review of the literature, 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, random walks in random environments, random dynamical systems and non-stationary systems.

ISBN: 9783031326011

Standard No.: 10.1007/978-3-031-32601-1doiSubjects--Topical Terms:

646262
Limit theorems (Probability theory)

LC Class. No.: QA273.67

Dewey Class. No.: 519.2

Local limit theorems for inhomogeneous Markov chains
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520 $a This book extends the local central limit theorem to inhomogeneous 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. It 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 numerous examples, a comprehensive review of the literature, 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, random walks in random environments, random dynamical systems and non-stationary systems.
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