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

Sefika Kuzgun; David Nualart

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arXiv · 2205.14024

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

Sefika Kuzgun·David Nualart

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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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Sefika Kuzgun, David Nualart. 2022-05-27. Convergence of densities of spatial averages of the parabolic Anderson model driven by colored noise. https://arxiv.org/abs/2205.14024

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