A Mean Field Approximation of the Bolker - Pacala Population Model
2014, v.20, №2, 329-348
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