Explicit Stationary Distribution of the(L,1)-reflecting Random Walk on the Half Line  

作　　者：Wen Ming HONG Ke ZHOU Yi Qiang Q.ZHAO 

机构地区：[1]School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems,Beijing Normal University [2]School of Mathematics and Statistics,Carleton University

出　　处：《Acta Mathematica Sinica,English Series》2014年第3期371-388,共18页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11131003);the Natural Sciences and Engineering Research Council of Canada(Grant No.315660)

摘　　要：In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.

关 键 词：Random walk multi-type branching process RECURRENCE positive recurrence stationarydistribution tail asymptotic 

分 类 号：O211.3[理学—概率论与数理统计]