Diffusion limits for a nonlinear density dependent space-time population model

Abstract

A population density process is constructed using approximately $N\imath$ particles performing rate $N^2$ random walks between N cells distributed on the unit interval. Particles give birth or die within cells, and particle death rates are a function of the occupied cell population. With suitable scaling, two possible limiting stochastic partial differential equations are obtained. Both are nonlinear perturbations of the equation satisfied by the density process of super Brownian motion.