Mathematical Sciences: Research in Stochastic Differential Equations

两位主要研究人员将继续在随机微分几何领域开展工作。Pinsky教授将考虑三个问题：黎曼流形中小测地线球的退出时间和退出位置的独立性；线性随机微分方程的随机稳定性负曲率流形上的谱渐近性。许教授将考虑小时间内热核的行为。这两位研究者的工作是在概率和几何分析的界面上进行的，其中一个领域的工具可以用来回答另一个领域的问题。

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.