Generalized Gambler’s Ruin Problem: Explicit Formulas via Siegmund Duality

被引：0
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作者：
Paweł Lorek
机构：
[1] University of Wrocław,Mathematical Institute
来源：
Methodology and Computing in Applied Probability | 2017年 / 19卷
关键词：
Generalized gambler’s ruin problem; Markov chains; Absorption probability; Siegmund duality; Möbius monotonicity; Partial ordering; 60J10; 60G40; 60J80;
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摘要：
We give explicit formulas for ruin probabilities in a multidimensional Generalized Gambler’s ruin problem. The generalization is best interpreted as a game of one player against d other players, allowing arbitrary winning and losing probabilities (including ties) depending on the current fortune with particular player. It includes many previous other generalizations as special cases. Instead of usually utilized first-step-like analysis we involve dualities between Markov chains. We give general procedure for solving ruin-like problems utilizing Siegmund duality in Markov chains for partially ordered state spaces studied recently in context of Möbius monotonicity.
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页码：603 / 613
页数：10
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