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

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

Nonparametric estimation of the death rate in branching diffusions


Code(s) de Classification MSC:

Résumé: We consider finite systems of diffusing particles in $\RR$ with branching and immigration. Branching of particles occurs at position dependent rate. Under ergodicity assumptions, we wish to estimate an unknown position-dependent branching rate based on observation of the particle process over a long time interval. We introduce kernel estimates for the branching rate and discuss their asymptotics with help of local time for the particle configuration. Depending on smoothness classes for the branching rate, we get non-parametric rates of convergence and prove that these rates are optimal in a minimax sense.

Mots Clés: branching diffusions ; nonparametric estimation ; kernel estimation

Date: 2000-03-20

Prépublication numéro: PMA-577