---

＜電子ブック＞
Markov Chains on Metric Spaces : A Short Course / by Michel Benaïm, Tobias Hurth
(Universitext. ISSN:21916675)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XV, 197 p. 1 illus : online resource
著者標目	*Benaïm, Michel author Hurth, Tobias author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Dynamical systems FREE:Probability Theory FREE:Dynamical Systems
一般注記	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 onMarkov 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 HTTP:URL=https://doi.org/10.1007/978-3-031-11822-7

 類似資料