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

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

LAN and LAMN for systems of interacting diffusions with branching and immigration

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider parametric models for finite systems of branching diffusions with interactions and immigration of particles. Under conditions which link together the asymptotic behaviour of the process of particle configurations with smoothness of the parametrisation, we prove local asymptotic normality or local asymptotic mixed normality as the observation time tends to infinity. The limit theorems which are used follow from dividing the trajectory of the process of particle configurations into independent life-cycles between successive visits of the void configuration.

Mots Clés: branching diffusions ; particle systems ; local asymptotic normality ; local asymptotic mixed normality

Date: 2000-04-26

Prépublication numéro: PMA-590