Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits

TL;DR

This paper develops higher order fluctuation expansions for nonlinear stochastic heat equations under singular limits, providing detailed asymptotic descriptions for various SPDEs including Dawson-Watanabe and Dean-Kawasaki models.

Contribution

It introduces Edgeworth-type expansions for SHE with diverse noise types, covering regular and irregular diffusion coefficients, advancing understanding of their asymptotic behaviors.

Findings

Derived asymptotic fluctuation expansions for SHE with different noise types

Included models like Dawson-Watanabe and Dean-Kawasaki in the analysis

Provided insights into the behavior of solutions in singular regimes

Abstract

Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint scaling regimes of small noise intensity and diverging singularity. The results include both the case of the SHE with regular and irregular diffusion coefficients. In particular, this includes the correlated Dawson-Watanabe and Dean-Kawasaki SPDEs, as well as SPDEs corresponding to the Fleming-Viot and symmetric simple exclusion processes.