论文标题
平均2D随机波方程
Averaging 2d stochastic wave equation
论文作者
论文摘要
我们考虑由高斯噪声驱动的2D随机波方程，该方程是暂时白色的，由Riesz内核描述。我们的第一个主要结果是溶液的空间平均值的功能性中心极限定理。而且我们还建立了边缘的定量中心极限定理，并且收敛速率由总变化距离描述。我们证明中的基本要素是Malliavin衍生产品的$ l^p $ estimate，它具有独立的利益。
We consider a 2D stochastic wave equation driven by a Gaussian noise, which is temporally white and spatially colored described by the Riesz kernel. Our first main result is the functional central limit theorem for the spatial average of the solution. And we also establish a quantitative central limit theorem for the marginal and the rate of convergence is described by the total-variation distance. A fundamental ingredient in our proofs is the pointwise $L^p$-estimate of Malliavin derivative, which is of independent interest.
