报告题目:Matching upper and lower moment bounds for a large class of stochastic PDEs driven by general
space-time Gaussian noises
报告人:胡耀忠 (University of Alberta)
报告时间:6月28日 10:00
报告地点:管理楼1418
摘要:
In this talk, I will present a joint work with Xiong Wang about the matching upper and lower moment bounds for the solution of stochastic partial differential equations driven by a general Gaussian noises, which gives a complete answer to the open problem of the matching lower moment bounds for the stochastic wave equations for general Gaussian noises. In order to to assure this intermittency property we introduce two new general conditions for the Green's function of the equation: small ball nondegeneracy and bounded Hardy-Littlewood-Sobolev total mass, which are satisfied by a large class of stochastic PDEs, including stochastic heat equations, stochastic wave equations, stochastic heat equations with fractional Laplacians, and stochastic partial differential equations with fractional derivatives both in time and in space. The main technique to obtain the lower moment bounds is to develop a Feynman diagram formula for the moments of the solution, to find the manageable main terms, and to carefully analyse these terms of sophisticated multiple integrals by exploring the above two properties.