Affine Dunkl processes

Abstract : We introduce the analogue of Dunkl processes in the case of an affine root system of type $\widetilde{\text{A}}_1$. The construction of the affine Dunkl process is achieved by a skew-product decomposition by means of its radial part and a jump process on the affine Weyl group, where the radial part of the affine Dunkl process is defined as the unique solution of some stochastic differential equation. We prove that the affine Dunkl process is a càdlàg Markov process as well as a local martingale, study its jumps, and give a martingale decomposition, which are properties similar to those of the classical Dunkl process.
Keywords :
Type de document :
Pré-publication, Document de travail
2010
Domaine :

https://hal.archives-ouvertes.fr/hal-00527315
Contributeur : Francois Chapon <>
Soumis le : lundi 18 octobre 2010 - 18:58:06
Dernière modification le : lundi 29 mai 2017 - 14:22:06
Document(s) archivé(s) le : mercredi 19 janvier 2011 - 02:54:26

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AffineDunkl.pdf
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Identifiants

• HAL Id : hal-00527315, version 1
• ARXIV : 1010.3680

Citation

Francois Chapon. Affine Dunkl processes. 2010. <hal-00527315>

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