Fluctuation Limits of a locally regulated population and generalized Langevin equations

Mladen Savov; Shidong Wang

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arXiv · 1411.2166

Fluctuation Limits of a locally regulated population and generalized Langevin equations

Mladen Savov·Shidong Wang

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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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Mladen Savov, Shidong Wang. 2014-11-08. Fluctuation Limits of a locally regulated population and generalized Langevin equations. https://arxiv.org/abs/1411.2166

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