The Annals of Probability

A chaotic representation property of the multidimensional Dunkl processes

Léonard Gallardo and Marc Yor

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Abstract

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.

Article information

Source
Ann. Probab., Volume 34, Number 4 (2006), 1530-1549.

Dates
First available in Project Euclid: 19 September 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1158673326

Digital Object Identifier
doi:10.1214/009117906000000133

Mathematical Reviews number (MathSciNet)
MR2257654

Zentralblatt MATH identifier
1107.60015

Subjects
Primary: 60G17: Sample path properties 60G44: Martingales with continuous parameter 60J25: Continuous-time Markov processes on general state spaces 60J60: Diffusion processes [See also 58J65] 60J65: Brownian motion [See also 58J65] 60J75: Jump processes 60H05: Stochastic integrals

Keywords
Markov processes with jumps Dunkl operators Dunkl processes intertwined semigroups Bessel processes normal martingales martingale decomposition generalized Hermite space–time polynomials Wiener chaos decomposition

Citation

Gallardo, Léonard; Yor, Marc. A chaotic representation property of the multidimensional Dunkl processes. Ann. Probab. 34 (2006), no. 4, 1530--1549. doi:10.1214/009117906000000133. https://projecteuclid.org/euclid.aop/1158673326


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