Mathematical Sciences: Diffusion Processes and Related Topics

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The principal investigator will continue his research in probability theory and classical analysis. Using and developing techniques in classical analysis (i.e. Dirichlet forms), he intends to obtain more precise approximations to certain transition probability functions. Furthermore, he will continue to simplify and extend known results in the area of large deviations, with an eye to applying these results to the analysis of stochastic processes which arise in Ising-type models of statistical mechanics. In this effort, the principal investigator will collaborate with a postdoctoral associate.