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July 2006 A chaotic representation property of the multidimensional Dunkl processes
Léonard Gallardo, Marc Yor
Ann. Probab. 34(4): 1530-1549 (July 2006). DOI: 10.1214/009117906000000133


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.


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Léonard Gallardo. Marc Yor. "A chaotic representation property of the multidimensional Dunkl processes." Ann. Probab. 34 (4) 1530 - 1549, July 2006.


Published: July 2006
First available in Project Euclid: 19 September 2006

zbMATH: 1107.60015
MathSciNet: MR2257654
Digital Object Identifier: 10.1214/009117906000000133

Primary: 60G17 , 60G44 , 60H05 , 60J25 , 60J60 , 60J65 , 60J75

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

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 4 • July 2006
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