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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J60 Diffusion processes, See also {58G32}

**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*