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A microscopic probabilistic description of a locally regulated population and macroscopic approximations
- Source :
- Annals of Applied Probability, Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2004, 14 (4), ⟨10.1214/105051604000000882⟩, Annals of Applied Probability, 2004, 14 (4), ⟨10.1214/105051604000000882⟩, Ann. Appl. Probab. 14, no. 4 (2004), 1880-1919
- Publication Year :
- 2004
- Publisher :
- HAL CCSD, 2004.
-
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.<br />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)
- 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
Subjects
Details
- Language :
- English
- ISSN :
- 10505164, 21688737, and 18801919
- Database :
- OpenAIRE
- Journal :
- Annals of Applied Probability, Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2004, 14 (4), ⟨10.1214/105051604000000882⟩, Annals of Applied Probability, 2004, 14 (4), ⟨10.1214/105051604000000882⟩, Ann. Appl. Probab. 14, no. 4 (2004), 1880-1919
- Accession number :
- edsair.doi.dedup.....529be7d493c4150b4fcf07a0d3d91110