Short Time Heat Kernel Behavior and the Multiplicative Stochastic Heat Equation
Hongyi Chen, University of Illinois-Chicago
Abstract: We show that a necessary and sufficient condition for existence and uniqueness of the Multiplicative Stochastic Heat Equation derived in previous work on specific compact Riemannian manifolds is in fact sharp for all compact Riemannian manifolds. The key observation needed to improve the argument in the previous cases is that different heat kernel upper bounds are needed when estimating the Brownian Bridge density accurately when the endpoints are close or far away from each other. Based on ongoing joint work with Robert Neel (Lehigh) and Cheng Ouyang (UIC). Time permitting, I will talk about some open problems and the potential role of geometry in them.
