Skew-product representations of multidimensional Dunkl Markov processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 4, p. 593-611

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.

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.

DOI : https://doi.org/10.1214/07-AIHP108
Classification:  60J75,  60J25
Keywords: Dunkl processes, Feller processes, Skew-product, Weyl group
@article{AIHPB_2008__44_4_593_0,
     author = {Chybiryakov, Oleksandr},
     title = {Skew-product representations of multidimensional Dunkl Markov processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {4},
     year = {2008},
     pages = {593-611},
     doi = {10.1214/07-AIHP108},
     zbl = {1180.60072},
     mrnumber = {2446290},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2008__44_4_593_0}
}
Chybiryakov, Oleksandr. Skew-product representations of multidimensional Dunkl Markov processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 4, pp. 593-611. doi : 10.1214/07-AIHP108. http://www.numdam.org/item/AIHPB_2008__44_4_593_0/

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