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

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

A microscopic probabilistic description of a locally regulated population and macroscopic approximations


Code(s) de Classification MSC:

Résumé: We consider a discrete model of locally regulated spatial population with mortality selection, introduced by Bolker and Pacala, [2]. We first generalize this model by adding spatial dependence, and give a pathwise description in terms of Poisson point measures. We then show that different renormalizations may lead to different macroscopic approximations of this model. We consider two specific cases. The first approximation is deterministic and gives a rigorous sense to the number density; the second one is a measure-valued process already studied by Etheridge [5]. Finally, we study in particular cases the long time behaviour of the system and reasonnable equilibria for the deterministic approximation.

Mots Clés: Interacting measure-valued processes ; Regulated population ; Deterministic macroscopic approximation ; Nonlinear superprocess ; Equilibrium

Date: 2003-02-27

Prépublication numéro: PMA-798

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