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

TL;DR

This paper derives integral representations and Laplace transforms for the reciprocal of the first hitting time of dihedral wedge boundaries by radial Dunkl processes, extending previous results to all even dihedral groups.

Contribution

It provides new integral formulas and extends existing results to all even dihedral groups for the hitting time distribution of radial Dunkl processes.

Findings

Integral representation for the density of the reciprocal first hitting time

Laplace transform expressed via Lauricella functions

Extension of previous results to all even dihedral groups

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.