A chaotic representation property of the multidimensional Dunkl processes

Details A chaotic representation property of the multidimensional Dunkl processes A chaotic representation property of the multidimensional Dunkl processes

2006-09-25

arxiv.org/abs/math/0609679v1

Annals of Probability 2006, Vol. 34, No. 4, 1530-1549

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000133 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000133

Dunkl processes are martingales as well as c\`{a}dl\`{a}g homogeneous Markov processes taking values in $\mathbb{R}^d$ 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 $L^2$ spaces of these processes in terms of adequate mixed multiple stochastic integrals.

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