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 Electronic Journal of Probability > Vol. 4 (1999) > Paper 15 open journal systems 


The Law of the Maximum of a Bessel Bridge

Jim Pitman, University of California, Berkeley
Marc Yor, Université Pierre et Marie Curie


Abstract
Let $M_d$ be the maximum of a standard Bessel bridge of dimension $d$. A series formula for $P(M_d le a)$ due to Gikhman and Kiefer for $d = 1,2, ldots$ is shown to be valid for all real $d >0$. Various other characterizations of the distribution of $M_d$ are given, including formulae for its Mellin transform, which is an entire function. The asymptotic distribution of $M_d$ is described both as $d$ tends to infinity and as $d$ tends to zero.


Full text: PDF

Pages: 1-35

Published on: May 26, 1999
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Electronic Journal of Probability. ISSN: 1083-6489