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The law of the maximum of a Bessel bridge. (English) Zbl 0943.60084

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 \(\delta\downarrow \infty\).

MSC:

60J65 Brownian motion
60J60 Diffusion processes
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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