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.
Publié le : 2006-07-14
Classification:
Markov processes with jumps,
Dunkl operators,
Dunkl processes,
intertwined semigroups,
Bessel processes,
normal martingales,
martingale decomposition,
generalized Hermite space–time polynomials,
Wiener chaos decomposition,
60G17,
60G44,
60J25,
60J60,
60J65,
60J75,
60H05
@article{1158673326,
author = {Gallardo, L\'eonard and Yor, Marc},
title = {A chaotic representation property of the multidimensional Dunkl processes},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 1530-1549},
language = {en},
url = {http://dml.mathdoc.fr/item/1158673326}
}
Gallardo, Léonard; Yor, Marc. A chaotic representation property of the multidimensional Dunkl processes. Ann. Probab., Tome 34 (2006) no. 1, pp. 1530-1549. http://gdmltest.u-ga.fr/item/1158673326/