Un théorème de Ray-Knight lié au supremum des temps locaux browniens

Abstract

Let α denote the first hitting time of 1 by the supremum, over nonnegative values of the space variable, of the Brownian local times. We give a complete description in terms of Bessel processes for the law of the process (in the space variable) of the Brownian local times at time α. The proofs rely on stochastic calculus, excursion theory and especially the Ray-Knight Theorems on Brownian local times. This result is applied to give a different proof of Borodin's result concerning the law of the supremum of Brownian local times taken at an independent exponential time.