Last exit decompositions and regularity at the boundary of transition probabilities

Abstract

The purpose of this paper is to give a probabilistic approach to studying the regularity at the boundary of the transition probabilities of certain hypoelliptic diffusions with boundary conditions. The main tools are last exit decompositions of Brownian motion, the Malliavin calculus, the theory of excursions, and the calculus of variations on Brownian excursions.