34. chen.ouyang.ea:23:parabolic#
Parabolic Anderson model with colored noise on torus
Le Chen, Cheng Ouyang, William Vickery
To appear in Bernoulli
Abstract: We construct an intrinsic family of Gaussian noises on the \(d\)-dimensional flat torus \(\mathbb{T}^d\). It is the analogue of the colored noise on \(\mathbb{R}^d\) and allows us to study stochastic PDEs on the torus in the Itô sense in high dimensions. With this noise, we consider the parabolic Anderson model (PAM) with measure-valued initial conditions and establish some basic properties of the solution, including a sharp upper and lower bound for the moments and Hölder continuity in space and time. The study of the toy model of \(\mathbb{T}^d\) in the present paper is a first step in our effort to understand how geometry and topology play a role in the behavior of stochastic PDEs on general (compact) manifolds.
MSC 2010 subject classifications: Primary 60H15, Secondary: 60G60, 37H15.
Keywords: stochastic heat equation on torus; Dalang’s condition; measure-valued initial condition; Brownian bridge; moment asymptotics; intermittency; moment Lyapunov exponent; theta function.
[COV23] Le Chen, Cheng Ouyang & William Vickery (2023) ‘Parabolic Anderson model with colored noise on torus’, preprint arXiv:2308.10802
@article{chen.ouyang.ea:23:parabolic,
title = {Parabolic Anderson model with colored noise on torus},
author = {Le Chen and Cheng Ouyang and William Vickery},
year = {2023},
month = {August},
journal = {preprint arXiv:2308.10802},
url = {http://arXiv.org/abs/2308.10802}
}
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