A Mean Field Approximation of the Bolker-Pacala Population Model

Mariya Bessonov; Stanislav Molchanov; Joseph Whitmeyer

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arXiv · 1302.1169

A Mean Field Approximation of the Bolker-Pacala Population Model

Mariya Bessonov·Stanislav Molchanov·Joseph Whitmeyer

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Abstract

We approximate the Bolker-Pacala model of population dynamics with the logistic Markov chain and analyze the latter. We find the asymptotics of the degenerated hypergeometric function and use these to prove a local CLT and large deviations result. We also state global limit theorems and obtain asymptotics for the first passage time to the boundary of a large interval.

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Mariya Bessonov, Stanislav Molchanov, Joseph Whitmeyer. 2013-12-12. A Mean Field Approximation of the Bolker-Pacala Population Model. https://arxiv.org/abs/1302.1169

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