论文标题
随机分数热方程的定量正常近似
Quantitative normal approximations for the stochastic fractional heat equation
论文作者
论文摘要
在本文中，我们介绍了由一般高斯乘法噪声驱动的随机分数热方程的{\ IT定量}中心限制定理，包括时空白噪声的案例和带有Riesz Kernel或有界整合功能的空间共价的白色噪声的情况。我们表明，半径$ r $收敛的空间平均值，因为在合适的重归于后，$ r $倾向于无穷大，在总变化距离处达到高斯极限。我们还提供功能性的中心限制定理。因此，我们最近将随机热方程式的结果扩展到了分数拉普拉斯式的情况和一般噪声的情况。
In this article we present a {\it quantitative} central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space-time white noise and the white-colored noise with spatial covariance given by the Riesz kernel or a bounded integrable function. We show that the spatial average over a ball of radius $R$ converges, as $R$ tends to infinity, after suitable renormalization, towards a Gaussian limit in the total variation distance. We also provide a functional central limit theorem. As such, we extend recently proved similar results for stochastic heat equation to the case of the fractional Laplacian and to the case of general noise.
