Stochastic Processes and Semilinear Partial Differential Equations

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9971009This 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.