• 科學研究
    報告題目:

    Asymptotic behavior of multiscale stochastic partial differential equations

    報告人:

    解龍杰 教授(江蘇師范大學)

    報告時間:

    報告地點:

    騰訊會議 ID:499 754 904 會議密碼:123456

    報告摘要:

    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.

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