Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

On a triplet of exponential Brownian functionals

Auteur(s):

Code(s) de Classification MSC:

Résumé: We study the three-dimensional joint distribution of a Brownian motion and the integrals of its exponentials from some points of view. We show an explicit expression of the Laplace transform of the distribution and the result gives an extension of Yor's result on the two-dimensional one. We apply the result to some problems, in particular, to the calculation of an explicit form of the heat kernel of the semigroup generated by the Maass Laplacian on the Poincaré upper half plane.

Mots Clés: Brownian motion ; Brownian functional ; heat kernel ; Maass Laplacian

Date: 2000-03-22

Prépublication numéro: PMA-578