应用数学所
学术报告


浏览次数:

 
Speaker:

解龙杰,江苏师范大学

Inviter: 朱湘婵 研究员
Title:
Averaging principle and normal deviations for multiscale stochastic systems
Time & Venue:

2020.12.7 16:00 Zoom会议: 942 676 4296 密码:123456

Abstract:

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 qutie 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. Thisis based on a joint work with Michael R?ckner.

Affiliation:  

学术报告中国科学院数学与系统科学研究院应用数学研究所
地址 北京市海淀区中关村东路55号 思源楼6-7层 南楼5-6、8层 100190
?2000-2013 京ICP备05058656号