Higher order fluctuation expansions for nonlinear stochastic heat equations in singular limits

Benjamin Gess, Zhengyan Wu and Rangrang Zhang

Stochastic Processes and their Applications, 2026, vol. 193, issue C

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 (ε → 0) and diverging singularity (δ → 0). 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.

Keywords: Small noise asymptotic expansions; Edgeworth expansion; Conservative SPDEs; Irregular coefficients; Higher order fluctuation (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104847

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