Gaussian fluctuations for the wave equation under rough random perturbations

Balan, Raluca M., Huang, Jingyu, Wang, Xiong, Xia, Panqiu and Yuan, Wangjun 2025. Gaussian fluctuations for the wave equation under rough random perturbations. Stochastic Processes and their Applications 182 , 104569. 10.1016/j.spa.2025.104569

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Abstract

In this article, we consider the stochastic wave equation in spatial dimension d = 1 , with linear term σ ( u ) = u multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with Hurst index H ∈ ( 1 4 , 1 2 ) . First, we prove that the solution is strictly stationary and ergodic in the spatial variable. Then, we show that with proper normalization and centering, the spatial average of the solution converges to the standard normal distribution, and we estimate the rate of this convergence in the total variation distance. We also prove the corresponding functional convergence result.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by/4.0/, Start Date: 2025-01-17
Publisher:	Elsevier
ISSN:	0304-4149
Date of First Compliant Deposit:	22 January 2025
Date of Acceptance:	9 January 2025
Last Modified:	22 Jan 2025 10:00
URI:	https://orca.cardiff.ac.uk/id/eprint/175498

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