Prof Yimin Xiao : Fractal Properties of Stochastic Heat Equations

Posted by Min Yang , part of the Statistics and Data Science Seminar.

At

Nov. 21, 2012, 4 p.m.

In

SEO 636

Abstract

By applying methods for studying Gaussian random fields, we investigate various analytic and fractal properties of the solutions of the stochastic heat equations driven by space-time white noise or fractional colored noise. These include fractal dimensions, exact modulus of continuity, hitting probabilities and existence of intersections. The proofs of these results are based on the properties of strong local nondeterminism. (Based on the on-going joint works with R. Dalang, C. Mueller and C. Tudor.)