Stochastic Processes and Semilinear Partial Differential Equations

9970942这是E·B·戴金(康奈尔大学)和S·E·库兹涅佐夫(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与一类半线性偏微分方程间的关系。该程序包括最近发展的概率工具在基本问题上的应用，如通过边界迹刻画正解和边界奇异性的分类。超扩散是一类特殊的分枝度量值随机过程，也称为超过程。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。除了纯粹的数学，它们在种群遗传学中扮演着重要的角色，它们为研究具有无限多个自由度的复杂物理系统提供了新的工具。这些研究人员将继续他们关于超扩散和涉及二阶非线性函数的微分方程之间的关系的联合工作。该研究计划包括最近开发的边界奇点概率分类的应用。

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.