Stochastic Processes and Semilinear Partial Differential Equations

随机过程和半线性偏微分方程

• 批准号: 9970942
• 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: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970942&HistoricalAwards=false
• 关键词: Stochastic; Processes; Semilinear; Partial; Differential

9970942This is a joint project of E. B. Dynkin (Cornell University) and S. E. Kuznetsov (University of Colorado, Boulder). The investigators will continue their work on relations between superdiffusions and a class of semilinear partial differential equations. The program includes applications of recently developed probabilistic tools to fundamental problems on such equations as a characterization of positive solutions by their boundary traces and a classification of boundary singularities.Superdiffusions are a special class of branching measure-valued stochastic processes also known as superprocesses. During the last decades these processes attracted efforts of many investigators around the world. Outside of pure mathematics, they play a significant role in population genetics and they provide new tools for the study of complex physical systems with infinitely many degrees of freedom. These researchers will continue their joint work on relations between superdiffusions and differential equations involving a second order nonlinear function. The research program includes applications of recently developed probabilistic classifications of boundary singularities.

9970942这是 E. B. Dynkin（康奈尔大学）和 S. E. Kuznetsov（科罗拉多大学博尔德分校）的联合项目。 研究人员将继续研究超扩散和一类半线性偏微分方程之间的关系。 该程序包括将最近开发的概率工具应用于此类方程的基本问题，例如通过边界迹来表征正解以及边界奇点的分类。超扩散是一类特殊的分支测值随机过程，也称为超级过程。 在过去的几十年里，这些过程吸引了世界各地许多研究人员的努力。 除了纯数学之外，它们在群体遗传学中发挥着重要作用，并为研究具有无限多个自由度的复杂物理系统提供了新工具。 这些研究人员将继续共同研究超扩散和涉及二阶非线性函数的微分方程之间的关系。 该研究计划包括最近开发的边界奇点概率分类的应用。