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

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

A trivariate law for certain processes related to perturbed Brownian motions


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