A Central Limit Theorem for the stochastic wave equation with fractional noise
Probability
2020-10-27 v3
Abstract
We study the one-dimensional stochastic wave equation driven by a Gaussian multiplicative noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter in the spatial variable. We show that the normalized spacial average of the solution over converges in total variation distance to a normal distribution, as tends to infinity. We also provide a functional central limit theorem.
Keywords
Cite
@article{arxiv.1812.05019,
title = {A Central Limit Theorem for the stochastic wave equation with fractional noise},
author = {Francisco Delgado-Vences and David Nualart and Guangqu Zheng},
journal= {arXiv preprint arXiv:1812.05019},
year = {2020}
}
Comments
V3: Typos fixed, a reference for two-parameter Clark-Ocone formula is added