报告题目： Fractal and Local Properties of Stochastic Heat Equations
                                            
报告人：   Yimin Xiao  Michigan State University
                                      
报告时间： 11/15 周三 下午4-5点

报告地点： 1518

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.