Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem

TL;DR

This paper develops new criteria for moment bounds in SPDEs driven by non-Gaussian noise, enabling the extension of regularity structures and proving a generalized Wong-Zakai theorem.

Contribution

It introduces streamlined criteria for stochastic estimates in non-Gaussian SPDEs, broadening the applicability of regularity structures and related theorems.

Findings

Established moment bounds for non-Gaussian SPDEs

Generalized Wong-Zakai Theorem for non-Gaussian noise

Facilitated analysis of phase coexistence models

Abstract

Upon its inception the theory of regularity structures allowed for the treatment for many semilinear perturbations of the stochastic heat equation driven by space-time white noise. When the driving noise is non-Gaussian the machinery of theory can still be used but must be combined with an infinite number of stochastic estimates in order to compensate for the loss of hypercontractivity. In this paper we obtain a more streamlined and automatic set of criteria implying these estimates which facilitates the treatment of some other problems including non-Gaussian noise such as some general phase coexistence models - as an example we prove here a generalization of the Wong-Zakai Theorem found by Hairer and Pardoux.