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

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

Bessel process with random drift and the $\frac{\langle X\rangle }{X}$ transformation

Auteur(s):

Code(s) de Classification MSC:

Résumé: We introduce here a class of processes which generalize the\textit{\ }Bessel processes with drift $\uparrow $ and $\downarrow $ introduced by S. Watanabe and further studied by J.W. Pitman and M. Yor. We show that for these processes there is a Lamperti representation defining a new class of ''exponential processes'' $X$ for which the process $\frac{\langle X\rangle }{X}$ is a diffusion in its own filtration.

Mots Clés: Bessel processes with drift ; Lamperti relations ; Exponential analogue of the $2M-X$ Pitman's theorem

Date: 2001-02-09

Prépublication numéro: PMA-637