Speaker: Pro.Yimin Xiao（Michigan State University）

Title: Introduction to Stochastic Partial Differential Equations

Time: May.6 & May.8 & May.9, 2019, PM:2:30-6:00

Location: Room 4318, Building No.4, Wushan Campus(Mar.6 & Mar.8)

               Room 4224, Building No.4, Wushan Campus(Mar.9)

Time & Location of Discussion: Mar.10, PM:2:30-6:00, Room 4226

Abstract:

      Limsup random fractals arise naturally in studying multifractal behavior of sample paths of stochastic processes such as Brownian motion, Levy processes, and Gaussian processes, and in problems related to random covering. These random sets are fundamentally different from random Cantor set, or ranges of Brownian motion, and have not been very well studied.

     In this lecture series, we will provide a general framework for studying the Hausdorff and packing dimensions of limsup random fractals, and their hitting probabilities. We will apply these results to characterize the fractal properties of the set of ``fast points for Gaussian processes, as well as the properties of random covering sets.