Mathematical Sciences: Construction and Study of Certain Infinite Dimensional Processes

数学科学：某些无限维过程的构造和研究

• 批准号: 8903474
• 负责人: Peter March
• 金额: $ 1.9万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-15 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903474&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Construction; Study; Certain

The principal investigator will study several models which arise in science in the study of growth, spread and development of a system of like particles. The evolution of these systems is random and can be conveniently described as a stochastic process with an infinite dimensional state space. The investigator will study these models by formulating and solving appropriate martingale problems then using the martingale framework to prove various limit theorems.

首席研究员将研究科学中出现的几个模型，这些模型研究类似粒子系统的生长、扩散和发展。这些系统的演化是随机的，可以方便地描述为具有无限维状态空间的随机过程。研究人员将通过建立和解决适当的鞅问题来研究这些模型，然后使用鞅框架来证明各种极限定理。