Annals of Applied Probability

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

Nicolas Fournier and Sylvie Méléard

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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.

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Ann. Appl. Probab., Volume 14, Number 4 (2004), 1880-1919.

First available in Project Euclid: 5 November 2004

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Interacting measure-valued processes regulated population deterministic macroscopic approximation nonlinear superprocess equilibrium


Fournier, Nicolas; Méléard, Sylvie. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14 (2004), no. 4, 1880--1919. doi:10.1214/105051604000000882.

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