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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

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

**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*