论文标题
平均原理和多尺度随机双曲线 - 促羟基方程的正常偏差
Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations
论文作者
论文摘要
我们研究具有缓慢和快速时间尺度的随机双曲抛物线方程的渐近行为。平均Principe中的强和弱收敛均已建立，可以看作是大量功能定律。然后，我们研究原始系统围绕其平均方程的随机波动。我们表明，归一化差异薄弱地收敛到线性随机波方程的解，这是功能性中心极限定理的一种形式。我们通过使用希尔伯特空间中的泊松方程为上述收敛提供了统一的证明。此外，还获得了尖锐的收敛速率，这些收敛性不取决于快速变量方程中系数的规律性。
We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large numbers. Then we study the stochastic fluctuations of the original system around its averaged equation. We show that the normalized difference converges weakly to the solution of a linear stochastic wave equation, which is a form of functional central limit theorem. We provide a unified proof for the above convergence by using the Poisson equation in Hilbert spaces. Moreover, sharp rates of convergence are obtained, which are shown not to depend on the regularity of the coefficients in the equation for the fast variable.
