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The distribution of Brownian quantiles

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Marc Yor
Marc Yor*
Affiliation:
Université Paris VI
*
∗Postal address: Laboratoire de Probabilités, Université Paris VI, 4, place Jussieu, Tour 56, 3ème Etage, 75252 Paris CEDEX 05, France.
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Abstract

The distribution of Brownian quantiles is determined, simplifying related integral expressions obtained by Lévy [9], [10] and more recently by Miura [11]. Three proofs are given, two of them involving last-passage times of Brownian motion, before time 1, at a given level.

Keywords

ARC-SINE LAWBETA AND GAMMA VARIABLES

MSC classification

Primary: 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 405 - 416
Copyright
Copyright © Applied Probability Trust 1995 

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References

References

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