Mathematical Sciences: Interacting Superprocesses

数学科学：相互作用的超级过程

• 批准号: 9015708
• 负责人: Steven Evans
• 金额: $ 3.78万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1992-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9015708&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Interacting; Superprocesses

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.

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，它作为粒子群的高密度限制而出现，其演化方式使得粒子总数以临界、连续时间、高尔顿-沃森分支过程的形式增长，而在诞生/死亡之间，粒子以独立的布朗运动移动。 这项研究的目标是为两个群体构建类似的模型，其中包含局部交互项。 这些额外项的重要性是为了捕捉竞争效应，其中一个群体中个体的存在会对来自其他群体中的个体成功复制自身的机会产生不利影响。