Open Access
2021 Averaging 2d stochastic wave equation
Raul Bolaños Guerrero, David Nualart, Guangqu Zheng
Author Affiliations +
Electron. J. Probab. 26: 1-32 (2021). DOI: 10.1214/21-EJP672


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 Lp-estimate of Malliavin derivative, which is of independent interest.

Funding Statement

David Nualart is supported by the NSF Grant DMS 1811181.


We are grateful to two referees for their critical comments that improved our work.


Download Citation

Raul Bolaños Guerrero. David Nualart. Guangqu Zheng. "Averaging 2d stochastic wave equation." Electron. J. Probab. 26 1 - 32, 2021.


Received: 7 December 2020; Accepted: 27 June 2021; Published: 2021
First available in Project Euclid: 14 July 2021

Digital Object Identifier: 10.1214/21-EJP672

Primary: 60F05 , 60G15 , 60H07 , 60H15

Keywords: central limit theorem , Malliavin-Stein method , Riesz kernel , Stochastic wave equation

Vol.26 • 2021
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