论文标题
多尺度随机部分微分方程的渐近行为
Asymptotic behavior of multiscale stochastic partial differential equations
论文作者
论文摘要
在本文中，我们研究了具有单数系数的半线性慢速随机部分微分方程的渐近行为。使用希尔伯特空间中的泊松方程，我们首先建立了平均Principe的强烈收敛，可以将其视为大数量的功能定律。然后，我们研究原始系统与其平均方程之间的随机波动。我们表明，归一化差异薄弱地收敛到Ornstein-Uhlenbeck类型过程，可以将其视为功能性中心极限定理。此外，获得了强收敛和正常偏差的收敛速率，并且这些收敛性不取决于等式中的系数的规律性，因为在限制系统中，快速变量与直觉相吻合，因为在极限系统中，快速组件已经完全均值或同性化。
In this paper, 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.
