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November 1996 A gambling system and a Markov chain
S. N. Ethier
Ann. Appl. Probab. 6(4): 1248-1259 (November 1996). DOI: 10.1214/aoap/1035463331

Abstract

"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 $p \geq 1/2$.

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S. N. Ethier. "A gambling system and a Markov chain." Ann. Appl. Probab. 6 (4) 1248 - 1259, November 1996. https://doi.org/10.1214/aoap/1035463331

Information

Published: November 1996
First available in Project Euclid: 24 October 2002

zbMATH: 0876.60051
MathSciNet: MR1422985
Digital Object Identifier: 10.1214/aoap/1035463331

Subjects:
Primary: 60J10 , 60J20

Keywords: Foster's criterion , Gambling system , Markov chain , recurrence , transience

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 4 • November 1996
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