Gaussian fluctuations for the stochastic heat equation with colored noise
Probability
2019-07-16 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1903.02509,
title = {Gaussian fluctuations for the stochastic heat equation with colored noise},
author = {Jingyu Huang and David Nualart and Lauri Viitasaari and Guangqu Zheng},
journal= {arXiv preprint arXiv:1903.02509},
year = {2019}
}
Comments
21pages; a new Corollary 3.3 is added for non-constant initial condition; the condition "sigma(1) is nonzero" is discussed; minor revision