Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Exchangeable Fragmentation-Coalescence processes and their equilibrium measures

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Code(s) de Classification MSC:

Résumé: We define and study a family of Markov processes with state space the compact set of all partitions of $\N$ that we call exchangeable fragmen\-tation-coalescence processes. They can be viewed as a combination of exchangeable fragmentation as defined by Bertoin and of homogenous coalescence as defined by Pitman and Schweinsberg or Möhle and Sagitov. We show that they admit a unique invariant probability measure and we study some properties of their paths and of their equilibrium measure.

Mots Clés: Fragmentation ; coalescence ; invariant distribution

Date: 2004-03-09

Prépublication numéro: PMA-890