报告人：解龙杰
报告地点：腾讯会议ID:238 293 120
报告时间：2022年11月11日星期五9:00-10:30
报告摘要:
We study the asymptotic behavior for an multiscale stochastic dynamical system with irregular 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.
主讲人简介：
解龙杰，江苏师范大学数学与统计学院教授，获得第十四届钟家庆数学奖，第七届江苏省数学成就奖。目前研究方向为随机分析及其应用/随机微分方程/Levy 过程，在相关领域做出重要工作。
