Reciprocal of the First Hitting Time of the Boundary of Dihedral Wedges by a Radial Dunkl Process

#### N. Demni

2017, v.23, Issue 4, 661-678

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 function and establish similar results for odd dihedral wedges.

Keywords: generalized Bessel function; dihedral groups; Gegenbauer polynomials; modified Bessel functions; radial Dunkl process; first hitting time of the boundary of a dihedral wedge