Open Access
1999 The Law of the Maximum of a Bessel Bridge
Jim Pitman, Marc Yor
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Electron. J. Probab. 4: 1-35 (1999). DOI: 10.1214/EJP.v4-52


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 $d \gt 0$. 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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Jim Pitman. Marc Yor. "The Law of the Maximum of a Bessel Bridge." Electron. J. Probab. 4 1 - 35, 1999.


Accepted: 26 May 1999; Published: 1999
First available in Project Euclid: 4 March 2016

zbMATH: 0943.60084
MathSciNet: MR1701890
Digital Object Identifier: 10.1214/EJP.v4-52

Primary: 60J65
Secondary: 33C10 , 60J60

Keywords: Bessel process , Brownian bridge , Brownian excursion , Brownian scaling , Local time , Riemann zeta function , zeros of Bessel functions

Vol.4 • 1999
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