A chaotic representation property of the multidimensional Dunkl processes

Abstract

Dunkl processes are martingales as well as càdlàg homogeneous Markov processes taking values in ℝ^d and they are naturally associated with a root system. In this paper we study the jumps of these processes, we describe precisely their martingale decompositions into continuous and purely discontinuous parts and we obtain a Wiener chaos decomposition of the corresponding L² spaces of these processes in terms of adequate mixed multiple stochastic integrals.