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

作　　者：Ya Zhe ZHANG Xian Yuan WU 

机构地区：[1]School of Mathematical Sciences,Capital Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第10期1939-1948,共10页数学学报（英文版）

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 countable- state space S = {1, 2,...}. Let T C S be an arbitrary finite subset of S. Denote by Ln the length of the longest run of consecutive i＇s for i E T, that occurs in the sequence X1,..., Xn. In this paper, we obtain a limit law and a week version of an Erd6s Rdnyi type law for Ln. A large deviation result of Ln is also discussed.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 countable- state space S = {1, 2,...}. Let T C S be an arbitrary finite subset of S. Denote by Ln the length of the longest run of consecutive i＇s for i E T, that occurs in the sequence X1,..., Xn. In this paper, we obtain a limit law and a week version of an Erd6s Rdnyi type law for Ln. A large deviation result of Ln is also discussed.

关 键 词：Longest run Stein-Chen method Poisson approximation 

分 类 号：O211.62[理学—概率论与数理统计] P228[理学—数学]