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

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

Asymptotic laws for nonconservative self-similar fragmentations


Code(s) de Classification MSC:

Résumé: We consider a self-similar fragmentation process in which the generic particle of mass $x$ is replaced by the offspring particles at probability rate $x^\alpha$, with positive parameter $\alpha$. The total of offspring masses may be both larger or smaller than $x$ with positive probability. We show that under certain conditions the typical mass in the ensemble is of the order $t^{-1/\alpha}$ and that the empirical distribution of masses converges to a random limit which we characterise in terms of the reproduction law.

Mots Clés: Strong asymptotic laws ; self-similar fragmentation

Date: 2004-02-13

Prépublication numéro: PMA-882