Tail asymptotic of the stationary distribution for the state dependent (1,R)-reflecting random walk: near critical

2013/02/13 by Wenming Hong, Ke Zhou, Hong, Wenming +1
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1302.3069

openalex publication_date 2013/02/13 · arxiv created 2013/02/26 · arxiv updated 2013/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the (1,R) state-dependent reflecting random walk (RW) on the half line, allowing the size of jumps to the right at maximal R and to the left only 1. We provide an explicit criterion for positive recurrence and the explicit expression of the stationary distribution based on the intrinsic branching structure within the walk. As an application, we obtain the tail asymptotic of the stationary distribution in the "near critical" situation.

Citations

• Branching structure for an (L-1) random walk in random environment and its applications

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