| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: D. Williams' path decomposition and Pitman's representation theorem for $BES(3)$ are expressions of some deep relations between reflecting Brownian motion and the $3$-dimensional Bessel process.\\ We present here some attempt to relate better reflecting Brownian motion and the $2$-dimensional Bessel process, using space and time changes related to the Ray-Knight theorems on local times, in the manner of Jeulin [19] and Biane-Yor [5].\\ The results provide some new understanding of the generalizations of Lévy's arc sine law obtained by the second author for perturbed Brownian motions.
Mots Clés: Reflecting Brownian motion ; Bessel processes ; Ray-Knight theorems ;
generalized arc-sine laws
Date: 1999-07-09
Prépublication numéro: PMA-519