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Markov chains on metric spaces = a s...

Benaim, Michel.

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Markov chains on metric spaces = a short course /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Markov chains on metric spaces/ by Michel Benaim, Tobias Hurth.
其他題名:	a short course /
作者:	Benaim, Michel.
其他作者:	Hurth, Tobias.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xv, 197 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Markov processes. -
電子資源:	https://doi.org/10.1007/978-3-031-11822-7
ISBN:	9783031118227

Markov chains on metric spaces = a 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

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

532104
Markov processes.

LC Class. No.: QA274.7

Dewey Class. No.: 519.233

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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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