DMS Stochastic Analysis Seminar

Speaker: Yaozhong Hu, Centennial Professor, University of Alberta at Edmonton, Canada (https://sites.ualberta.ca/~yaozhong/)

Title: The lower moment bounds for a large class of stochastic PDEs driven by fractional space-time noises

Abstract: In this talk I will present some upper and lower moment bounds for various stochastic PDEs with varieties of space-time Gaussian noises. These bounds match each other on the exponential scale. Due to the absence of the powerful Feynman-Kac formula, the lower moment bounds have been missing for many interesting equations except for the stochastic heat equation. Our work introduces and explores the Feynman diagram formula for the moments of the solution and the small ball nondegeneracy for the Green's function to obtain the lower bounds for all moments which match the upper moment bounds. The equations are wide and include stochastic wave equations, stochastic heat equations with fractional Laplacian, and stochastic diffusions which are both fractional in time and in space.

This is a joint work with Xiong Wang.