Introduction

First hitting time of the boundary of a wedge of angle pi/4 by a radial Dunkl process

“…Indeed, its angular part was identified there with a time-changed real Jacobi process by an independent Bessel clock and this identification was the key ingredient in proving several probabilistic and analytic results such as the expressions of the semi-group density and of the generalized Bessel function, a skew-product decomposition and the tail distribution of the first hitting time of the boundary of a dihedral wedge. In particular, the expansion in the basis of Jacobi polynomials obtained for the tail distribution generalizes the known Fourier expansions for the tail distribution of the exit time from dihedral wedges by a planar Brownian motion ( [3], [5]). However, this expansion is not quite satisfactory since for instance its non negativity is far from being obvious.…”

“…In this section, we give a particular interest to the exit time of a planar Brownian motion from a dihedral wedge which already attracted the attention of probabilists and physicists. For instance, the tail distribution of this random variable was derived in [9] using the reflection principle and combinatorial arguments, and in an unpublished manuscript by A. Comtet who solved the heat equation in an arbitrary wedge with Dirichlet boundary conditions ( [5]). Another expression of this probability was also obtained in [3] for arbitrary wedges as a series of modified Bessel functions.…”