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

• 成果类型: Article
• 署名作者: Fournier, N; Méléard, S
• 署名单位: Universite de Lorraine; Universite Paris Nanterre
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000882
• 发表日期: 2004
• 页码: 1880-1919
• 关键词: branching-processes; moment equations; WEAK-CONVERGENCE

摘要

We consider a discrete model that describes a locally regulated spatial population with mortality selection. This model was studied in parallel by Bolker and Pacala and Dieckmann, Law and Murrell. We first generalize this model by adding spatial dependence. Then we give a pathwise description in terms of Poisson point measures. We show that different normalizations may lead to different macroscopic approximations of this model. The first approximation is deterministic and gives a rigorous sense to the number density. The second approximation is a superprocess previously studied by Etheridge. Finally, we study in specific cases the long time behavior of the system and of its deterministic approximation.