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The Heckman–Opdam Markov processes
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  • Published: 07 November 2006

The Heckman–Opdam Markov processes

  • Bruno Schapira1,2 

Probability Theory and Related Fields volume 138, pages 495–519 (2007)Cite this article

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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).

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Author information

Authors and Affiliations

  1. Fédération Denis Poisson, Laboratoire MAPMO, Université d’Orléans, B.P. 6759, 45067, Orléans cedex 2, France

    Bruno Schapira

  2. Laboratoire de Probabilités et Modéles Aléatoires, Université Pierre et Marie Curie, 4 place Jussieu, F-75252, Paris cedex 05, France

    Bruno Schapira

Authors
  1. Bruno Schapira
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Corresponding author

Correspondence to Bruno Schapira.

Additional information

Partially supported by the European Commission (IHP Network HARP 2002–2006).

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Schapira, B. The Heckman–Opdam Markov processes. Probab. Theory Relat. Fields 138, 495–519 (2007). https://doi.org/10.1007/s00440-006-0034-1

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  • Received: 10 May 2006

  • Revised: 05 October 2006

  • Published: 07 November 2006

  • Issue Date: July 2007

  • DOI: https://doi.org/10.1007/s00440-006-0034-1

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Keywords

  • Markov processes
  • Jump processes
  • Root systems
  • Dirichlet forms
  • Dunkl processes
  • Limit theorems

Mathematical Subject Classification (2000)

  • 58J65
  • 60B15
  • 60F05
  • 60F17
  • 60J35
  • 60J60
  • 60J65
  • 60J75
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