Gambler's ruin and the first exit position of random walk from large spheres (Q1345605)
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scientific article; zbMATH DE number 731988
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gambler's ruin and the first exit position of random walk from large spheres |
scientific article; zbMATH DE number 731988 |
Statements
Gambler's ruin and the first exit position of random walk from large spheres (English)
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31 August 1995
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Let \(T_ r\) be the first time a sum \(S_ n\) of nondegenerated i.i.d. \(d\)-dimensional random vectors leaves the sphere of radius \(r\). The behavior of \(S(T_ r)\) is investigated for \(d = 1\) and \(d > 1\). The results give the solution of some general gambler's ruin problems.
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random walk
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gambler's ruin
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overshoot
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