Asymptotic Behavior of Multiscale Stochastic Partial Differential Equations

  • [2020-11-02]

    Speaker:  XIE Longjie

                    Jiangsu Normal University

    Time: 2020-11-02, 16:00-17:00

    Place (virtual): Tencent Meeting ID: 704 539 612, Password: 123456

    Organizer: School of Mathematical Sciences



    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 principe, 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.



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