A Mean Field Approximation of the Bolker - Pacala Population Model

M. Bessonov, S.A. Molchanov, J. Whitmeyer

2014, v.20, №2, 329-348

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.

Keywords: Bolker - Pacala model,logistic Markov chain,limit theorems

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