Skew-product representations of multidimensional Dunkl Markov processes

TL;DR

This paper develops skew-product representations for multidimensional Dunkl processes, extending known one-dimensional decompositions, and investigates the properties of Dunkl martingales and the radial component within Weyl chambers.

Contribution

It introduces a multidimensional skew-product decomposition for Dunkl processes, generalizing previous one-dimensional results and analyzing the radial part's behavior.

Findings

Established skew-product representations for multidimensional Dunkl processes.

Analyzed properties of Dunkl martingales.

Studied the radial part of Dunkl processes in Weyl chambers.

Abstract

In this paper we obtain skew-product representations of the multidimensional Dunkl processes which generalize the skew-product decomposition in dimension 1 obtained in L. Gallardo and M. Yor. Some remarkable properties of the Dunkl martingales. S\'{e}minaire de Probabilit\'{e}s XXXIX, 2006. We also study the radial part of the Dunkl process, i.e. the projection of the Dunkl process on a Weyl chamber.