A trivariate law for certain processes related to perturbed Brownian motions

Abstract

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. In [Ph. Carmona et al., Stochastic Process. Appl. 7 (1999) 323-333], we presented an 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 [Lect.