A GAMBLING SYSTEM AND A MARKOV CHAIN
成果类型：
Article
署名作者：
Ethier, S. N.
署名单位：
Utah System of Higher Education; University of Utah
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
1248-1259
关键词：
摘要：
Oscar's system is a gambling system in which the aim is to win one betting unit, at least with high probability, and then start over again. The system can be modeled by an irreducible Markov chain in a subset of the two-dimensional integer lattice. We show that the Markov chain, which depends on a parameter p representing the single-trial win probability, is transient if p < 1/2 and positive recurrent if p >= 1/2