The 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 5 November 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1099674082

Digital Object Identifier
doi:10.1214/105051604000000882

Mathematical Reviews number (MathSciNet)
MR2099656

Zentralblatt MATH identifier
1060.92055

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1099674082


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