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:** 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*