The Heckman–Opdam Markov processes |
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Authors: | Bruno Schapira |
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Institution: | (1) Fédération Denis Poisson, Laboratoire MAPMO, Université d’Orléans, B.P. 6759, 45067 Orléans cedex 2, France;(2) Laboratoire de Probabilités et Modéles Aléatoires, Université Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris cedex 05, France |
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Abstract: | We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale
decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers, a central limit
theorem, and the convergence of the normalized process to the Dunkl process. Eventually we describe the asymptotic behavior
of the infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric spaces setting in (Iberoamericana 18: 41–97,
2002).
Partially supported by the European Commission (IHP Network HARP 2002–2006). |
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Keywords: | Markov processes Jump processes Root systems Dirichlet forms Dunkl processes Limit theorems |
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