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.
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