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.

马尔可夫过程理论的研究将是 集中研究分支测度值过程， 函数空间中的相关过程。 的一般形式 分支，路径属性之间的关系， 超扩散与非线性微分方程正解 具有相互作用部分的“随机云”的方程和建模 是调查的主要目标之一。 测度值分支过程的研究始于 20世纪60年代末， 在过去的五年里。 这是一个了不起的班级， 过程，为调查提供了一种工具， 空间分布的人口。 它们还使得有可能 扩展了概率论和 偏微分方程理论