Gaussian fluctuations for the stochastic heat equation with colored noise
Gaussian fluctuations for the stochastic heat equation with colored noise
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DOI：
10.1007/s40072-019-00149-3
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发表时间：
2020-06-01
影响因子：
1.5
通讯作者：
Zheng, Guangqu
中科院分区：
文献类型：
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作者：
Huang, Jingyu;Nualart, David;Zheng, Guangqu
本文给出了由高斯乘性噪声驱动的d维随机热方程的一个定量中心极限定理，该方程在时间上是白色的，并且具有由Riesz核给出的空间协方差。我们证明了当球的半径趋于无穷大时，欧几里得球上解的空间平均值接近高斯分布。利用Malliavin演算和Stein方法，在总变差距离中描述了中心极限定理。我们还给出了一个泛函中心极限定理。
In this paper, we present a quantitative central limit theorem for the d-dimensional stochastic heat equation driven by a Gaussian multiplicative noise, which is white in time and has a spatial covariance given by the Riesz kernel. We show that the spatial average of the solution over an Euclidean ball is close to a Gaussian distribution, when the radius of the ball tends to infinity. Our central limit theorem is described in the total variation distance, using Malliavin calculus and Stein's method. We also provide a functional central limit theorem.