澳门金沙网址

科学研究
报告题目:

Asymptotic behavior of multiscale stochastic partial differential equations

报告人:

解龙杰 教授(江苏师范大学)

报告时间:

报告地点:

腾讯会议 ID:499 754 904 会议密码:123456

报告摘要:

We study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the averaging principle, which can be viewed as a functional law of large numbers. Then we study the stochastic fluctuations between the original system and its averaged equation. We show that the normalized difference converges weakly to an Ornstein-Uhlenbeck type process, which can be viewed as a functional central limit theorem. Furthermore, rates of convergence both for the strong convergence and the normal deviation are obtained, and these convergence are shown not to depend on the regularity of the coefficients in the equation for the fast variable, which coincides with the intuition, since in the limit systems the fast component has been totally averaged or homogenized out. This is based on a joint work with Michael Rockner and Li Yang.