Dunkl processes are martingales as well as càdlàg homogeneous Markov processes taking values in ℝd 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.
Léonard Gallardo. Marc Yor. "A chaotic representation property of the multidimensional Dunkl processes." Ann. Probab. 34 (4) 1530 - 1549, July 2006. https://doi.org/10.1214/009117906000000133