A mean field approximation of the Bolker-Pacala population model (Q2923171)

The Bolker-Pacala model is a stochastic spatial model in the theory of population dynamics. In the paper, the mean field approximation to the general Bolker-Pacala process is introduced. All particles live on the lattice \(\mathbb Z^d\). The total number of particles is a Markov process and is called the logistic Markov chain. The logistic Markov chain is a particular case of a birth-and-death random walk on \({\mathbb Z}^1_+ = \{0,1, \dots\}\) and is used to analyze the mean-field model. A local central limit Markov chain is obtained. Also, the authors state global limit theorems and obtain asymptotics for the first passage time to the boundary of a large interval.