20171115Fractal and Local Properties of Stochastic Heat Equations
摘要：Consider a system of linear stochastic heat equations driven by space-time white noise (or fractional-colored noise). Its mild solution, when exists, is a Gaussian random field. By applying methods on Gaussian random fields, we investigate various analytic and fractal properties of the solutions of the stochastic heat equations. 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. This talk is based on recent joint works with R. Dalang, C. Mueller, and C. Tudor.