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Titlebook: Markov Chains and Invariant Probabilities; Onésimo Hernández-Lerma,Jean Bernard Lasserre Book 2003 Birkh?user Verlag 2003 Markov chain.erg

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發(fā)表于 2025-3-21 19:39:19 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Markov Chains and Invariant Probabilities
編輯Onésimo Hernández-Lerma,Jean Bernard Lasserre
視頻videohttp://file.papertrans.cn/625/624619/624619.mp4
概述Some of the results presented appear for the first time in book form.Emphasis on the role of expected occupation measures to study the long-run behavior of Markov chains on uncountable spaces
叢書名稱Progress in Mathematics
圖書封面Titlebook: Markov Chains and Invariant Probabilities;  Onésimo Hernández-Lerma,Jean Bernard Lasserre Book 2003 Birkh?user Verlag 2003 Markov chain.erg
描述This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k‘ k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).
出版日期Book 2003
關(guān)鍵詞Markov chain; ergodicity; mathematical methods in physics; probability measure; probability theory
版次1
doihttps://doi.org/10.1007/978-3-0348-8024-4
isbn_softcover978-3-0348-9408-1
isbn_ebook978-3-0348-8024-4Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightBirkh?user Verlag 2003
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Progress in Mathematicshttp://image.papertrans.cn/m/image/624619.jpg
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PreliminariesIn this chapter we summarize some results from Real Analysis that will be extensively used in later chapters. As many of these results are standard, we do not include proofs of them, but we provide appropriate references.
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發(fā)表于 2025-3-22 18:27:28 | 只看該作者
Markov Chains in Metric SpacesWe now consider a MC in a LCS (locally compact separable) metric space . and with at least one invariant p.m., say . From a practical point of view, LCS metric spaces are very important as many, if not most, real-world applications fall into this framework.
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Strong and Uniform ErgodicityIn this chapter we introduce the notions of . and . of MCs. We study how these notions relate to the concept of “stability” of a transition kernel and to the solvability of the Poisson equation (8.2.1).
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發(fā)表于 2025-3-23 07:31:27 | 只看該作者
Existence and Uniqueness of Invariant Probability MeasuresA critical assumption for many results of previous chapters is that a MC admits at least one invariant p.m. In this chapter we investigate the issue of existence of those invariant p.m.’s.
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