Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

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

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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