The Heckman-Opdam Markov processes

Details The Heckman-Opdam Markov processes The Heckman-Opdam Markov processes

2006-04-30

arxiv.org/abs/math/0605020v1

Mathematics

Probability

Scientific paper

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 \cite{ABJ}.

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