Reciprocal of the First hitting time of the boundary of dihedral wedges by a radial Dunkl process

Abstract

In this paper, we establish an integral representation for the density of the reciprocal of the first hitting time of the boundary of even dihedral wedges by a radial Dunkl process having equal multiplicity values. Doing so provides another proof and extends to all even dihedral groups the main result proved in \cite{Demni1}. We also express the weighted Laplace transform of this density through the fourth Lauricella Lauricella function and establish a similar integral representation for odd dihedral wedges.