A central limit theorem for the stochastic heat equation
A central limit theorem for the stochastic heat equation
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DOI：
10.1016/j.spa.2020.07.010
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发表时间：
2020-12-01
影响因子：
1.4
通讯作者：
Viitasaari, Lauri
中科院分区：
文献类型：
--
作者：
Huang, Jingyu;Nualart, David;Viitasaari, Lauri
考虑乘性时空白色噪声驱动下的一维随机热方程。我们表明，空间积分的解决方案从-R R R收敛到一个标准的正态分布的总方差距离R趋于无穷大，重整化后。我们还展示了这个中心极限定理的功能版本。(C)2020爱思唯尔B. V.保留所有权利。
We consider the one-dimensional stochastic heat equation driven by a multiplicative space-time white noise. We show that the spatial integral of the solution from -R to R converges in total variance distance to a standard normal distribution as R tends to infinity, after renormalization. We also show a functional version of this central limit theorem. (C) 2020 Elsevier B.V. All rights reserved.