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Markov chains on metric spacesa short course /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Markov chains on metric spacesby Michel Benaim, Tobias Hurth.
Reminder of title:	a short course /
Author:	Benaim, Michel.
other author:	Hurth, Tobias.
Published:	Cham :Springer International Publishing :2022.
Description:	xv, 197 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Markov processes.
Online resource:	https://doi.org/10.1007/978-3-031-11822-7
ISBN:	9783031118227$q(electronic bk.)

Markov chains on metric spacesa short course /
Benaim, Michel.

Markov chains on metric spacesa short course /[electronic resource] :by Michel Benaim, Tobias Hurth. - Cham :Springer International Publishing :2022. - xv, 197 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

1 Markov Chains -- 2 Countable Markov Chains -- 3 Random Dynamical Systems -- 4 Invariant and Ergodic Probability Measures -- 5 Irreducibility -- 6 Petite Sets and Doeblin points -- 7 Harris and Positive Recurrence -- 8 Harris Ergodic Theorem.

This book gives an introduction to discrete-time Markov chains which evolve on a separable metric space. The focus is on the ergodic properties of such chains, i.e., on their long-term statistical behaviour. Among the main topics are existence and uniqueness of invariant probability measures, irreducibility, recurrence, regularizing properties for Markov kernels, and convergence to equilibrium. These concepts are investigated with tools such as Lyapunov functions, petite and small sets, Doeblin and accessible points, coupling, as well as key notions from classical ergodic theory. The theory is illustrated through several recurring classes of examples, e.g., random contractions, randomly switched vector fields, and stochastic differential equations, the latter providing a bridge to continuous-time Markov processes. The book can serve as the core for a semester- or year-long graduate course in probability theory with an emphasis on Markov chains or random dynamics. Some of the material is also well suited for an ergodic theory course. Readers should have taken an introductory course on probability theory, based on measure theory. While there is a chapter devoted to chains on a countable state space, a certain familiarity with Markov chains on a finite state space is also recommended.

ISBN: 9783031118227$q(electronic bk.)

Standard No.: 10.1007/978-3-031-11822-7doiSubjects--Topical Terms:

181910
Markov processes.

LC Class. No.: QA274.7

Dewey Class. No.: 519.233

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505 0 $a 1 Markov Chains -- 2 Countable Markov Chains -- 3 Random Dynamical Systems -- 4 Invariant and Ergodic Probability Measures -- 5 Irreducibility -- 6 Petite Sets and Doeblin points -- 7 Harris and Positive Recurrence -- 8 Harris Ergodic Theorem.
520 $a This book gives an introduction to discrete-time Markov chains which evolve on a separable metric space. The focus is on the ergodic properties of such chains, i.e., on their long-term statistical behaviour. Among the main topics are existence and uniqueness of invariant probability measures, irreducibility, recurrence, regularizing properties for Markov kernels, and convergence to equilibrium. These concepts are investigated with tools such as Lyapunov functions, petite and small sets, Doeblin and accessible points, coupling, as well as key notions from classical ergodic theory. The theory is illustrated through several recurring classes of examples, e.g., random contractions, randomly switched vector fields, and stochastic differential equations, the latter providing a bridge to continuous-time Markov processes. The book can serve as the core for a semester- or year-long graduate course in probability theory with an emphasis on Markov chains or random dynamics. Some of the material is also well suited for an ergodic theory course. Readers should have taken an introductory course on probability theory, based on measure theory. While there is a chapter devoted to chains on a countable state space, a certain familiarity with Markov chains on a finite state space is also recommended.
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