Fluctuation Limits of a locally regulated population and generalized Langevin equations

2014/11/08 by Mladen Savov, Savov, Mladen, Shidong Wang +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Evolution and Genetic Dynamics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1411.2166

23 pages

arxiv created 2014/11/08 · arxiv updated 2014/11/11

Abstract

We consider a locally regulated spatial population model introduced by Bolker and Pacala. Based on the deterministic approximation studied by Fournier and Méléard, we prove that the fluctuation theorem holds under some mild moment conditions. The limiting process is shown to be an infinite-dimensional Gaussian process solving a generalized Langevin equation. In particular, we further consider its properties in one-dimension case, which is characterized as a time-inhomogeneous Ornstein-Uhlenbeck process.

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