Probability Seminar

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

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.

Date: Tuesday, April 05, 2016
Time: 3:00PM
Where: Lunt 105
Contact Person: Qiang Zeng
Contact email:
Contact Phone:
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