Local Time and Excursions of Reflected Brownian Motion in a Wedge

Abstract

When the vertex is a regular point for reflected Brownian motion in a wedge, with a constant direction of reflection on each side of the wedge, the law of the excursions from the vertex is determined in the following sense. The nature of the local time at the vertex and the Laplace transform of the entrance law at that point are explicitly given. In parti-culai, it is shown that the inverse local time at the vertex is a stable subordinator of index α/2 where 0 <2. Here ξ is the angle of the wedge (0