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

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  • Gess, Benjamin
  • Wu, Zhengyan
  • Zhang, Rangrang

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.

Suggested Citation

  • Gess, Benjamin & Wu, Zhengyan & Zhang, Rangrang, 2026. "Higher order fluctuation expansions for nonlinear stochastic heat equations in singular limits," Stochastic Processes and their Applications, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:spapps:v:193:y:2026:i:c:s0304414925002911
    DOI: 10.1016/j.spa.2025.104847
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    References listed on IDEAS

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    1. Mandler, Christian & Overbeck, Ludger, 2022. "A functional Itō-formula for Dawson–Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 202-228.
    2. Ravishankar, K., 1992. "Fluctuations from the hydrodynamical limit for the symmetric simple exclusion in d," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 31-37, August.
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