Mathematical Sciences: Interacting Superprocesses

首席研究员将研究相互作用的超布朗运动。超布朗运动是一种测量值扩散，它产生于粒子种群的高密度极限，粒子总数以一种临界的、连续的、高尔顿-沃森分支过程的方式增长，而在出生/死亡之间，粒子以独立的布朗运动运动。本研究的目的是为两个包含局部交互项的种群构建相似的模型。这些额外术语的重要性在于捕捉竞争效应，即来自一个种群的个体的存在会对来自另一个种群的个体成功复制自己的机会产生不利影响。

The principal investigator will study interacting super- Brownian motions. Super-Brownian motion is a measure-valued diffusion that arises as a high density limit for a population of particles evolving in such a way that the total number of particles grows as a critical, continuous-time, Galton-Watson branching process, whilst in between births/deaths the particles move as independent Brownian motions. The goal of this research is to construct similar models for two populations which incorporate localized interaction terms. The import of these extra terms is to capture competition effects in which the presence of individuals from one population adversely affects the chance for individuals from the other population to successfully replicate themselves.