A chaotic representation property of the multidimensional Dunkl processes

Abstract

Dunkl processes are martingales as well as càdlàg 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.

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

References in corpus (2)

• Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators
• Skew-product representations of multidimensional Dunkl Markov processes

Cited by in corpus (11)

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• Skew-product representations of multidimensional Dunkl Markov processes
• Generalized Bessel function of Type D
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• Dimension-Free Square Function Estimates for Dunkl Operators
• Radial Dunkl Processes : Existence and uniqueness, Hitting time, Beta Processes and Random Matrices
• Dunkl jump processes: relaxation and a phase transition
• Weak Type Estimates for Square Functions of Dunkl Heat Flows
• Affine Dunkl processes
• Semilinear equations associated with Dunkl Laplacian