Mean Ruin Time for Gambler's Ruin Problem

机译：赌徒毁灭问题的平均毁灭时间

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In this note, we point out mean ruin time is a concept which is different from mean persisting gambled time and present theoretical and numerical solutions for mean ruin time of gambler's ruin problem. Then we employ Monte Carlo simulation to verify that mean ruin time of the gambler with less initial fortune is far less than mean persisting gambled time especially when his winning probability is close to his losing probability on each play of the game.

机译：在本说明中，我们指出了卑鄙的毁灭时间是一种与卑鄙赌博的时间不同的概念，并呈现赌徒毁灭问题的平均毁灭时间的理论和数值解决方案。然后，我们雇用了Monte Carlo模拟，以验证赌徒的平均毁灭时间与较少的财富较少的赌注时间远远不到卑鄙的赌博的时间，特别是当他的获胜概率接近他在每次游戏中的失去概率时。

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《International Conference on Business Computing and Global Informatization》|2011年||共4页
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Meiping Xu; Yuanwei Xu;
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中图分类 TP14-53;
关键词
Monte Carlo simulation; markov chain; mean persisting gambled time; mean ruin time;

机译：蒙特卡罗模拟;马尔可夫链;平均持续赌博的时间;平均毁灭时间;

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2. Moments of the Time of Ruin, Surplus Before Ruin and the Deficit at Ruin in the Erlang(N) Risk Process [J] . Yong-sheng Xing, Rong Wu Acta Mathematicae Applicatae Sinica . 2006,第4期

机译：Erlang（N）风险过程中的破产时间，破产前的盈余和破产赤字的时刻
3. Open Quantum Random Walks: Ergodicity, Hitting Times, Gambler's Ruin and Potential Theory [J] . Lardizabal Carlos F., Souza Rafael R. Journal of Statistical Physics . 2016,第5期

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4. Mean Ruin Time for Gambler's Ruin Problem [C] . Meiping Xu, Yuanwei Xu 2011 International Conference on Business Computing and Global Informatization . 2011

机译：赌徒破产问题的平均破产时间
5. Change -point detection of two -sided alternatives in the Brownian motion model and its connection to the gambler's ruin problem with relative wealth perception [D] . Hadjiliadis, Olympia. 2005

机译：布朗运动模型中双向选择的变化点检测及其与相对财富感知的赌徒破产问题的联系
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7. Open quantum random walks: ergodicity, hitting times, gambler's ruin and potential theory [O] . Lardizabal, Carlos F., Souza, Rafael R. 2016

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Mean Ruin Time for Gambler's Ruin Problem

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