On First Returning Time and Last Exit Time of a Class of Markov Chain  

作　　者：Hui Zeng ZHANG Min Zhi ZHAO Lei WANG 

机构地区：[1]Department of Mathematics,Hangzhou Normal University [2]Department of Mathematics,Zhejiang University

出　　处：《Acta Mathematica Sinica,English Series》2013年第2期331-344,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11001070,11101113);Zhejiang Provincial Natural Science Foundation(Grant No.R6090034)

摘　　要：Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent when μ 〈 1; is null recurrent when μ= 1; and is transient when μ 〉 1. In this paper, the integrability of the first returning time and the last exit time are discussed. Keywords Geom/G/1 queuing model, first returning time, last exit time, Markov chainLet {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent when μ 〈 1; is null recurrent when μ= 1; and is transient when μ 〉 1. In this paper, the integrability of the first returning time and the last exit time are discussed. Keywords Geom/G/1 queuing model, first returning time, last exit time, Markov chain

关 键 词：Geom/G/1 queuing model first returning time last exit time Markov chain 

分 类 号：O211.62[理学—概率论与数理统计] O412.1[理学—数学]