论文标题
非线性随机波方程的中央限制定理三维
Central limit theorems for nonlinear stochastic wave equations in dimension three
论文作者
论文摘要
在本文中，我们考虑了由白色的高斯噪声驱动的三维非线性随机波方程，该方程是白色的，并且具有一些空间相关性。使用Malliavin-Stein的方法，我们证明了在Wasserstein距离下解决方案的空间平均值的高斯波动，在空间相关性通过可集成函数和Riesz内核给出的情况下。在这两种情况下，我们还建立了功能性中心限制定理。
In this paper, we consider three-dimensional nonlinear stochastic wave equations driven by the Gaussian noise which is white in time and has some spatial correlations. Using the Malliavin-Stein's method, we prove the Gaussian fluctuation for the spatial average of the solution under the Wasserstein distance in the cases where the spatial correlation is given by an integrable function and by the Riesz kernel. In both cases we also establish functional central limit theorems.
