Speaker: Cheuk-Yin Lee (Chinese University of Hong Kong)

 

Title: Local times of Gaussian random fields and SPDEs

 

Abstract: Local times of stochastic processes are closely related to sample path irregularities and fractal and geometric properties of level sets. I will discuss two basic approaches for studying local times: one via Fourier transform and the other via chaos expansion. In particular, I will focus on the first approach in the case of Gaussian random fields and present some local time and related results which can be applied to the solutions of systems of linear SPDEs such as stochastic heat and wave equations. If time permits, I will briefly explain our research direction on local times of non-Gaussian processes with the second approach.

 

Host: Le Chen