Mathematical Sciences: Research in Stochastic Differential Equations

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The two principal investigators will continue work in the area of stochastic differential geometry. Professor Pinsky will consider three problems: independence of exit time and exit position from small geodesic balls in Riemannian manifolds; stochastic stability of linear stochastic differential equations; spectral asymptotics on manifolds of negative curvature. Professor Hsu will consider the behavior of the heat kernel for small times. The work that these two investigators conduct is at the interface of Probability and Geometric Analysis, where the tools from one area can be used to answer questions in the other.