Radial Dunkl processes associated with Dihedral systems

TL;DR

This paper investigates radial Dunkl processes linked to dihedral systems, deriving their semigroup, generalized Bessel functions, and Dunkl-Hermite polynomials, along with a decomposition and boundary hitting time distribution.

Contribution

It introduces new analytical tools for radial Dunkl processes with dihedral symmetry, including explicit formulas and probabilistic decompositions.

Findings

Derived the semigroup and generalized Bessel function for these processes.

Provided a skew product decomposition using independent Bessel processes.

Computed the tail distribution of the first hitting time of the Weyl chamber boundary.

Abstract

We stduy radial Dunkl processes associated with dihedral systems: we derive the semi group, the generalized Bessel function, the Dunkl-Hermite polynomials. Then we give a skew product decomposition by means of independent Bessel processes and we compute the tail distribution of the first hitting time of the boundary of Weyl chamber.