一、题目

Averaging principle and normal deviation for multiscale stochastic systems

二、主讲人

解龙杰

三、摘要

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with singular coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle of functional law of large numbers type are established. Then we consider the small fluctuations of the system around its average. Nine cases of functional central limit type theorems are obtained. In particular, even though the averaged equation for the original system is the same, the corresponding homogenization limit for the normal deviation can be quite different due to the difference in the interactions between the fast scales and the deviation scales. We provide quite intuitive explanations for each case. Furthermore, sharp rates both for the strong convergences and the functional central limit theorems are obtained, and these convergences are shown to rely only on the regularity of the coefficients of the system with respect to the slow variable, and do not depend on their regularity with respect to the fast variable, which coincide with the intuition since in the limit equations the fast component has been totally averaged or homogenized out. This is based on a joint work with Michael Roeckner.

四、主讲人简介

解龙杰，江苏师范大学教授，2011年本科毕业于中南大学，2016年博士毕业于武汉大学。2017-2018年在美国伊利诺伊大学香槟分校(UIUC)作访问学者，2018年-2020年在德国比勒费尔德大学作洪堡学者，2019年获第十四届钟家庆数学奖。主要研究方向包括非局部算子热核估计和奇异系数随机(偏)微分方程等，至今已在《Probab. Theory Rel. Fields》《Ann. Probab.》《Ann. Inst. Henri Poincare-Pr.》《Stoch. Proc. Appl.》《J. Diff. Equ.》等知名期刊上发表论文20篇。

五、邀请人

陈章 数学学院教授

六、时间

12月3日（周四）13:30-14:30

七、地点

腾讯会议，会议ID：706435159

八、主办方

山东大学数学学院