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学术预告:Yimin Xiao谈“ Fractal Properties of the Solution to Stochastic Heat Equations ”

作者:沈冬杰   点击:43  发布时间:2014-12-25 10:29:04

报告人 Prof. Yimin Xiao

       Department of Statistics and Probability

       Michigan State University

       USA

时间:20141229日上午9:30-10:30

地点:下沙校区教学D104(理学院党员之家)

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 the latter, 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. (Based on the on-going joint works with R. Dalang, C. Mueller and C. Tudor.)