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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
[2]Getoor, R. K. (1979) The Brownian escape process. Ann. Prob. 7, 864–867.Google Scholar
[3]Pitman, J. W. Et Yor, M. (1981) Bessel processes and infinitely divisible laws. In Stochastic Integrals, ed. Williams, D. Lecture Notes in Mathematics 851, Springer-Verlag, Berlin.Google Scholar
[4]Revuz, D. Et Yor, M. (1991) Continuous Martingales and Brownian Motion. Springer-Verlag, Berlin.Google Scholar
[5]Sharpe, M. (1980) Some transformations of diffusions by time reversal. Ann. Prob. 8, 1157–1162.Google Scholar
[6]Williams, D. (1974) Path decomposition and continuity of local time for one-dimensional diffusions. Proc. London Math. Soc. 28, 738–768.Google Scholar
[7]Yor, M. (1984) A propos de l'inverse du mouvement brownien dans ℝn (n ≧ 3). Ann. Inst. H. Poincaré 21, 27–38.Google Scholar
[8]Yor, M. (1990) Sur les décompositions affines d'une variable stable d'indice 1/2. En préparation.Google Scholar