English

Averaging 2d stochastic wave equation

Probability 2021-07-29 v2

Abstract

We consider a 2D stochastic wave equation driven by a Gaussian noise, which is temporally white and spatially colored described by the Riesz kernel. Our first main result is the functional central limit theorem for the spatial average of the solution. And we also establish a quantitative central limit theorem for the marginal and the rate of convergence is described by the total-variation distance. A fundamental ingredient in our proofs is the pointwise LpL^p-estimate of Malliavin derivative, which is of independent interest.

Keywords

Cite

@article{arxiv.2003.10346,
  title  = {Averaging 2d stochastic wave equation},
  author = {Raul Bolaños Guerrero and David Nualart and Guangqu Zheng},
  journal= {arXiv preprint arXiv:2003.10346},
  year   = {2021}
}

Comments

Version2:32pages, restructured, removed Lemma 3.4. and modified Lemma 3.3 (now Lemma 4.3), simplified Step-4, added Remark 3 and (4.8); version 1: 34pages

R2 v1 2026-06-23T14:24:10.868Z