Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Self-similar fragmentations

Auteur(s):

Code(s) de Classification MSC:

• 60J25 Markov processes with continuous parameter
• 60G09 Exchangeability

Résumé: We introduce a probabilistic model that is meant to describe an object that falls apart randomly as time passes and fulfills a certain scaling property. We show that the distribution of such a process is determined by its index of self-similarity $\alpha\in \R$, a rate of erosion $c\geq0$, and a so-called L\'evy measure that accounts for sudden dislocations. The key of the analysis is provided by a transformation of self-similar fragmentations which enables us to reduce the study to the homogeneous case $\alpha=0$ which is treated in [6]

Mots Clés: Fragmentation ; self-similar ; exchangeable partition

Date: 2000-09-08

Prépublication numéro: PMA-610