EVENT DETAILS AND ABSTRACT

Title: Non-uniqueness in SPDEs with non-Lipschitz noise coefficients
Speaker: Yu-Ting Chen
Speaker Info: Harvard University
Brief Description:
Special Note:
Abstract:

One problem for uniqueness in SPDEs, open for more than two decades, is to determine pathwise uniqueness in the SPDE of one-dimensional super-Brownian motion that features nonnegative solutions and a square-root noise coefficient. A positive result would establish an infinite-dimensional analogue of the celebrated Yamada-Watanabe sharp uniqueness for SDEs with non-Lipschitz noise coefficients. However, Mueller, Mytnik and Perkins (2013) prove that, among other things, dropping the assumption of nonnegative solutions leads to pathwise non-uniqueness. This result leaves open the question whether nonnegativity of solutions would be a mechanism sufficient for the uniqueness.

In this talk, I will discuss a result which continues the investigation of the SPDE of super-Brownian motion by Mueller et al. I will first review the SPDE of super-Brownian motion and related aspects. Then I will introduce certain perturbations for the SPDE, and discuss a non-uniqueness result for the nonnegative solutions of those perturbed SPDEs.