An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source

Davar Khoshnevisan; Kunwoo Kim; Carl Mueller

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arXiv · 2504.11107

An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source

Davar Khoshnevisan·Kunwoo Kim·Carl Mueller

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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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Davar Khoshnevisan, Kunwoo Kim, Carl Mueller. 2025-04-15. An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source. https://arxiv.org/abs/2504.11107

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