Convergence of densities of spatial averages of the parabolic Anderson model driven by colored noise

Sefika Kuzgun, David Nualart

Type: Article

Publication Date: 2023-07-26

Citations: 0

DOI: https://doi.org/10.1080/17442508.2023.2238954

Abstract

In this paper, we present a rate of convergence in the uniform norm for the densities of spatial averages of the solution to the d-dimensional parabolic Anderson model driven by a Gaussian multiplicative noise, which is white in time and has a spatial covariance given by the Riesz kernel. The proof is based on the combination of Malliavin calculus techniques and the Stein's method for normal approximations.

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