The law of the maximum of a Bessel bridge (Q1298340)
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scientific article; zbMATH DE number 1325998
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The law of the maximum of a Bessel bridge |
scientific article; zbMATH DE number 1325998 |
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The law of the maximum of a Bessel bridge (English)
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22 August 1999
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Let \(M_\delta\) be the maximum of a standard Bessel bridge of dimension \(\delta\). A series formula for \(P(M_\delta\leq a)\) due to Gikhman and Kiefer for \(\delta= 1,2,\dots\) is shown to be valid for all real \(\delta>0\). Various other characterizations of the distribution of \(M_\delta\) are given, including formulae for its Mellin transform, which is an entire function. The asymptotic distribution of \(M_\delta\) is described both as \(\delta\to \infty\) and as \(\delta\downarrow \infty\).
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Brownian brigde
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Brownian excursion
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Brownian scaling
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local time
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Bessel process
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zeros of Bessel functions
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Riemann zeta function
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