Work

Central limit theorems for stochastic wave equations in high dimensions

Year: 2025

Type: article

Abstract: We consider stochastic wave equations in spatial dimensions d≥4. We assume that the driving noise is given by a Gaussian noise that is white in time and has some spatial correlation. When the spatial correlation is given by the Riesz kernel, we establish that the spatial integral of the solution with proper normalization converges to the standard normal distribution under the Wasserstein distance. The convergence is obtained by first constructing the approximation sequence to the solution and then applying Malliavin-Stein’s method to the normalized spatial integral of the sequence. The corresponding functional central limit theorem is presented as well.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1319

Author: Masahisa Ebina

Institution: Kyoto University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: Japan Society for the Promotion of Science