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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.沉思的鱼 发表于 2025-3-22 18:27:28
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.壮丽的去 发表于 2025-3-23 00:55:57
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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).chiropractor 发表于 2025-3-23 07:31:27
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.