Some Results Associated with the, Longest Run in a Strongly Ergodic Markov Chain

作者：Ya; Zhe; ZHANG; Xian; Yuan; WU马尔可夫链连续运行强遍历可数状态空间有限子集大偏差法律可逆

摘要：This paper discusses the asymptotic behaviors of the longest run on a countable state Markov chain.Let {Xa} a∈Z + be a stationary strongly ergodic reversible Markov chain on countablestate space S = {1,2,...}.Let TS be an arbitrary finite subset of S.Denote by Ln the length of the longest run of consecutive i's for i∈T,that occurs in the sequence X1,...,Xn.In this paper,we obtain a limit law and a week version of an Erds-Rényi type law for Ln.A large deviation result of Ln is also discussed.

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