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

• 成果类型: Article
• 署名作者: Blount, D
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1996
• 页码: 639-659
• 关键词: partial-differential equations; chemical-reactions; fluctuations; systems

摘要

A population density process is constructed using approximately NI 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.