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

Author

Fournier, Nicolas and Meleard, Sylvie

Subjects
Mathematics - Probability, 60J80, 60K35. (Primary)
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., Comment: Published at http://dx.doi.org/10.1214/105051604000000882 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Published
2005
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2. A microscopic probabilistic description of a locally regulated population and macroscopic approximations

Author

Sylvie Méléard, Nicolas Fournier, Institut Élie Cartan de Nancy (IECN), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Approximations of π, Population, Interacting measure-valued processes, Poisson distribution, equilibrium, 01 natural sciences, deterministic macroscopic approximation, 010104 statistics & probability, symbols.namesake, FOS: Mathematics, Point (geometry), Statistical physics, 0101 mathematics, Spatial dependence, education, ComputingMilieux_MISCELLANEOUS, Superprocess, Mathematics, 60J80, education.field_of_study, Number density, Probability (math.PR), 010102 general mathematics, 16. Peace & justice, Probabilistic description, regulated population, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], nonlinear superprocess, 60K35, 60J80, 60K35. (Primary), symbols, Statistics, Probability and Uncertainty, Mathematics - Probability
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., Published at http://dx.doi.org/10.1214/105051604000000882 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Published
2004

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