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Sur certaines fonctionnelles exponentielles du mouvement brownien réel

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Marc Yor
Marc Yor*
Affiliation:
Université Paris VI
*
∗ Adresse postale: Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, Tour 56, 3ème Etage, 75252 Paris Cedex 05, France.
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Abstract

Dufresne [1] recently showed that the integral of the exponential of Brownian motion with negative drift is distributed as the reciprocal of a gamma variable. In this paper, it is shown that this result is another formulation of the distribution of last exit times for transient Bessel processes. A bivariate distribution of such integrals of exponentials is also obtained explicitly.

Keywords

GAMMA VARIABLEBESSEL PROCESSES

MSC classification

Primary: 60J65: Brownian motion
Secondary: 60J60: Diffusion processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 202 - 208
Copyright
Copyright © Applied Probability Trust 1992 

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References

[1]Dufresne, D. (1990) The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuarial J., 39–79.Google Scholar
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