Light-tailed behavior of stationary distribution for state-dependent random walks on a strip

doi:10.1007/s11464-014-0405-3

Front. Math. China

2014, Vol. 9

Issue (4) : 813-834 https://doi.org/10.1007/s11464-014-0405-3

RESEARCH ARTICLE

Light-tailed behavior of stationary distribution for state-dependent random walks on a strip

Wenming HONG¹,Meijuan ZHANG^2,^*(

),Yiqiang Q. ZHAO³

1. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, China
2. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China
3. School of Mathematics and Statistics, Carleton University, Ottawa, Ont K1S 5B6, Canada

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Abstract

We consider the state-dependent reflecting random walk on a halfstrip. We provide explicit criteria for (positive) recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed behavior of the stationary distribution is proved under appropriate conditions. The key idea of the method employed here is the decomposition of the trajectory of the random walk and the main tool is the intrinsic branching structure buried in the random walk on a strip, which is different from the matrix-analytic method.

Keywords Random walk on a strip stationary distribution light-tailed behavior branching process recurrence state-dependent

Corresponding Author(s): Meijuan ZHANG

Issue Date: 26 August 2014

Cite this article:

Wenming HONG,Meijuan ZHANG,Yiqiang Q. ZHAO. Light-tailed behavior of stationary distribution for state-dependent random walks on a strip[J]. Front. Math. China, 2014, 9(4): 813-834.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0405-3
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I4/813

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