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The Law of the Maximum of a Bessel Bridge


 
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1. Title Title of document The Law of the Maximum of a Bessel Bridge
 
2. Creator Author's name, affiliation, country Jim Pitman; University of California, Berkeley
 
2. Creator Author's name, affiliation, country Marc Yor; Université Pierre et Marie Curie
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian bridge, Brownian excursion, Brownian scaling, local time, Bessel process, zeros of Bessel functions, Riemann zeta function
 
3. Subject Subject classification 60J65, 60J60, 33C10
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1999-05-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/52
 
10. Identifier Digital Object Identifier 10.1214/EJP.v4-52
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 4
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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