书目名称 | Markov Chains on Metric Spaces | 副标题 | A Short Course | 编辑 | Michel Benaïm,Tobias Hurth | 视频video | | 概述 | A self-contained, mathematically rigorous presentation of the ergodic theory of Markov chains.Illustrates core notions through examples from current research.Helps the reader learn the material throug | 丛书名称 | Universitext | 图书封面 |  | 描述 | 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 withan 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 coun | 出版日期 | Textbook 2022 | 关键词 | Ergodic theory in probability; Ergodic theory for Markov chains; Random dynamical systems; invariant me | 版次 | 1 | doi | https://doi.org/10.1007/978-3-031-11822-7 | isbn_softcover | 978-3-031-11821-0 | isbn_ebook | 978-3-031-11822-7Series ISSN 0172-5939 Series E-ISSN 2191-6675 | issn_series | 0172-5939 | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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