论文标题
中心限制定理的随机波方程在一个和两个方面
Central limit theorems for stochastic wave equations in dimensions one and two
论文作者
论文摘要
修复$ d \ in \ {1,2 \} $，我们认为由高斯噪声驱动的$ d $二维随机波方程，该方程在空间上是白色的，在空间上是彩色的，因此空间相关功能是可以集成的，并且可以满足Dalang的状况。在这种情况下，我们为在欧几里得球上的溶液的空间平均值提供定量的中心限制，因为球的半径向无穷大。我们还建立了功能性中心限制定理。在我们的分析中，一种基本要素是该解决方案的Malliavin衍生物的点$ l^p $ estigate，这是独立的。本文是最近平均随机部分微分方程的研究行的另一个附录。
Fix $d\in\{1,2\}$, we consider a $d$-dimensional stochastic wave equation driven by a Gaussian noise, which is temporally white and colored in space such that the spatial correlation function is integrable and satisfies Dalang's condition. In this setting, we provide quantitative central limit theorems for the spatial average of the solution over a Euclidean ball, as the radius of the ball diverges to infinity. We also establish functional central limit theorems. A fundamental ingredient in our analysis is the pointwise $L^p$-estimate for the Malliavin derivative of the solution, which is of independent interest. This paper is another addendum to the recent research line of averaging stochastic partial differential equations.
