Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Skew-product representations of multidimensional Dunkl Markov processes

Oleksandr Chybiryakov

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Abstract

In this paper we obtain skew-product representations of the multidimensional Dunkl processes which generalize the skew-product decomposition in dimension 1 obtained in L. Gallardo and M. Yor. Some remarkable properties of the Dunkl martingales. Séminaire de Probabilités XXXIX, 2006. We also study the radial part of the Dunkl process, i.e. the projection of the Dunkl process on a Weyl chamber.

Résumé

Dans cet article nous obtenons des produits semi-directs des processus de Dunkl multidimensionnels qui généralisent ceux obtenus en dimension 1 dans L. Gallardo and M. Yor. Some remarkable properties of the Dunkl martingales. In Séminaire de Probabilités XXXIX, 2006. Nous étudions les processus de Dunkl radiaux qui sont les projections des processus de Dunkl sur une chambre de Weyl.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 4 (2008), 593-611.

Dates
First available in Project Euclid: 5 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1217964112

Digital Object Identifier
doi:10.1214/07-AIHP108

Mathematical Reviews number (MathSciNet)
MR2446290

Zentralblatt MATH identifier
1180.60072

Subjects
Primary: 60J75: Jump processes 60J25: Continuous-time Markov processes on general state spaces

Keywords
Dunkl processes Feller processes Skew-product Weyl group

Citation

Chybiryakov, Oleksandr. Skew-product representations of multidimensional Dunkl Markov processes. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 4, 593--611. doi:10.1214/07-AIHP108. https://projecteuclid.org/euclid.aihp/1217964112


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