An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source
Probability
2025-04-16 v1
Abstract
We establish a notion of universality for the parabolic Anderson model via an invariance principle for a wide family of parabolic stochastic partial differential equations. We then use this invariance principle in order to provide an asymptotic theory for a wide class of non-linear SPDEs. A novel ingredient of this invariance principle is the dissipativity of the underlying stochastic PDE.
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Cite
@article{arxiv.2504.11107,
title = {An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source},
author = {Davar Khoshnevisan and Kunwoo Kim and Carl Mueller},
journal= {arXiv preprint arXiv:2504.11107},
year = {2025}
}
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42 pages