English

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 H[1/2,1)H\in [1/2,1) in the spatial variable. We show that the normalized spacial average of the solution over [R,R][-R,R] converges in total variation distance to a normal distribution, as RR 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