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

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

Equilibrium for fragmentation with immigration


Code(s) de Classification MSC:

Résumé: This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and absence of stationary distributions are established and uniqueness is proved. Also, convergence rates to the stationary distribution are given. Linear equations which are the deterministic counterparts of fragmentation with immigration processes are next considered. As in the stochastic case, existence and uniqueness of solutions, as well as existence and uniqueness of stationary solutions, are investigated.

Mots Clés: Fragmentation ; immigration ; stationary distribution

Date: 2004-06-03

Prépublication numéro: PMA-918