论文标题
随机热方程系统的空间平均值的高斯波动
Gaussian fluctuations of spatial averages of a system of stochastic heat equations
论文作者
论文摘要
我们考虑一个由$ M $二维时空白噪声驱动的$ d $非线性随机热方程的系统，$ \ mathbb {r} _+\ times \ times \ mathbb {r} $。在本文中，我们研究了空间平均值的渐近行为在$ [-R，R] $的大间隔内。我们在Wasserstein距离和功能性中心极限定理中建立了与多元正态分布的收敛速率。
We consider a system of $d$ non-linear stochastic heat equations driven by an $m$-dimensional space-time white noise on $\mathbb{R}_+\times \mathbb{R}$. In this paper we study the asymptotic behavior of spatial averages over large intervals $[-R,R]$. We establish a rate of convergence to a multivariate normal distribution in the Wasserstein distance and a functional central limit theorem.
