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

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

Homogeneous fragmentation processes


Code(s) de Classification MSC:

Résumé: The purpose of this work is to define and study homogeneous fragmentation processes in continuous time, which are meant to describe the evolution of an object that breaks down randomly into pieces as time passes. Roughly, we show that the dynamic of such a fragmentation process is determined by some exchangeable measure on the set of partitions of $\N$, and results from the combination of two different phenomena: a continuous erosion and sudden dislocations. In particular, we determine the class of fragmentation measures which can arise in this setting, and investigate the evolution of the size of the fragment that contains a point pick at random at the initial time.

Mots Clés: Fragmentation ; exchangeable partitions ; subordinator

Date: 2000-04-26

Prépublication numéro: PMA-592