Mathematical Sciences: Branching Measure-Valued Stochastic Processes and Related Topics

数学科学：分支测值随机过程及相关主题

• 批准号: 9301315
• 负责人: Eugene Dynkin
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301315&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Branching; Measure; Valued

Investigations in the theory of Markov processes are to be done with concentration on branching measure-valued processes and related processes in spaces of functions. The general form of branching, the relationship between path properties of superdiffusions and positive solutions of nonlinear differential equations and modeling of "a random cloud" with interacting parts are among the principal objectives of the investigation. Measure-valued branching processes have been studied since the late 1960s and have attracted a great deal of attention during the last five years. This is a remarkable class of processes, which provide a tool for the investigation of spatially distributed populations. They also make it possible to extend important connections between probability theory and the theory of partial differential equations.

马尔可夫过程理论中的研究应集中于分支测量值的过程和功能空间中的相关过程。 分支的一般形式，即超级消防酶的路径特性与非线性微分方程的正溶液与与相互作用部分的“随机云”的建模是研究的主要目标之一。 自1960年代后期以来，已经研究了测量值的分支过程，并在过去五年中引起了很多关注。 这是一类非凡的过程，它为研究空间分布的人群提供了一种工具。 它们还使概率理论与部分微分方程理论之间的重要联系成为可能。