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Fluctuation limits of a locally regulated population and generalized Langevin equations

机译：局部调节种群的波动极限和广义Langevin方程

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摘要

We consider a locally regulated spatial population model introduced by Bolker and Pacala. Based on the deterministic approximation studied by Fournier and Meleard, 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.
机译：我们考虑由Bolker和Pacala引入的局部调控的空间人口模型。基于Fournier和Meleard研究的确定性近似，我们证明了波动定理在某些温和矩条件下成立。极限过程被证明是解决广义Langevin方程的无穷高斯过程。特别是，我们在一维情况下进一步考虑了其性质，这种情况被描述为时间不均匀的Ornstein-Uhlenbeck过程。

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