GAMBLER'S RUIN ESTIMATES ON FINITE INNER UNIFORM DOMAINS
成果类型：
Article
署名作者：
Diaconis, Persi; Houston-Edwards, Kelsey; Saloff-Coste, Laurent
署名单位：
Stanford University; Franklin W. Olin College of Engineering; Cornell University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/20-AAP1607
发表日期：
2021
页码：
865-895
关键词：
摘要：
Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform. Precisely, we show that gambler's ruin estimates reduce to a good understanding of the Perron-Frobenius eigenfunction and eigenvalue whenever the underlying chain and its Doob transform are Harnack Markov chains. Finite inner-uniform domains (say, in the square grid Z(n)) provide a large class of examples where these ideas apply and lead to detailed estimates. In general, understanding the behavior of the Perron-Frobenius eigenfunction remains a challenge.