| Explicit Stationary Distribution of the （L, 1）-reflecting Random Walk on the Half Line |
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| 引用本文： | Wen Ming HONG,Ke ZHOU,Yi Qiang Q. ZHAO. Explicit Stationary Distribution of the （L, 1）-reflecting Random Walk on the Half Line[J]. 数学学报(英文版), 2014, 30(3): 371-388. DOI: 10.1007/s10114-014-3009-7 |
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| 作者姓名： | Wen Ming HONG Ke ZHOU Yi Qiang Q. ZHAO |
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| 作者单位： | [1]School of Mathematical Sciences ＆ Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, P. R. China [2]School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada KIS 5B6 |
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| 基金项目： | Supported by National Natural Science Foundation of China(Grant No.11131003);the Natural Sciences and Engineering Research Council of Canada(Grant No.315660) |
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| 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.
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| 关 键 词： | 平稳分布 随机游走 半直线 反射 最大尺寸 渐近行为 分支结构 随机游动 |
Explicit stationary distribution of the (L, 1)-reflecting random walk on the half line |
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| Wen Ming Hong,Ke Zhou,Yi Qiang,Q. Zhao. Explicit stationary distribution of the (L, 1)-reflecting random walk on the half line[J]. Acta Mathematica Sinica(English Series), 2014, 30(3): 371-388. DOI: 10.1007/s10114-014-3009-7 |
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| Authors: | Wen Ming Hong Ke Zhou Yi Qiang Q. Zhao |
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| Affiliation: | 1. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, P. R. China
2. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada, K1S 5B6
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| Abstract: | 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. |
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| Keywords: | Random walk multi-type branching process recurrence positive recurrence stationary distribution tail asymptotic |
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