Favorite sites of a persistent random walk

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:501

Article

Ghosh, Arka¹  Noren, Steven²  Roitershtein, Alexander³ 

[1] Iowa State Univ, Dept Stat, Ames, IA 50011 USA

[2] Monmouth Coll, Dept Math & Comp Sci, Monmouth, IL USA

[3] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA

关键词: Favorite sites;    Most visited sites;    Local time;    Correlated random walks;    Discrete Ray-Knight theorems;   

DOI  :  10.1016/j.jmaa.2021.125180

来源: Elsevier

【 摘 要 】

We consider favorite (i.e., most visited) sites of a symmetric persistent random walk on Z, a discrete-time process typified by the correlation of its directional history. We show that the cardinality of the set of favorite sites is eventually at most three. This is a generalization of a result by Toth for a simple random walk, used to partially prove a longstanding conjecture by Erdos and Revesz. The original conjecture asserting that for the simple random walk on integers the cardinality of the set of favorite sites is eventually at most two was recently disproved by Ding and Shen. Published by Elsevier Inc.

【 授权许可】

Free