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

Benjamin Gess; Zhengyan Wu; Rangrang Zhang

doi:10.1016/j.spa.2025.104847

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

Benjamin Gess
, Zhengyan Wu^*
, Rangrang Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	104847
Journal	Stochastic Processes and their Applications
Volume	193
DOIs	https://doi.org/10.1016/j.spa.2025.104847
Publication status	Published - Mar 2026
Externally published	Yes

Keywords

Conservative SPDEs
Edgeworth expansion
Higher order fluctuation
Irregular coefficients
Small noise asymptotic expansions

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10.1016/j.spa.2025.104847

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title = "Higher order fluctuation expansions for nonlinear stochastic heat equations in singular limits",

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 = "Conservative SPDEs, Edgeworth expansion, Higher order fluctuation, Irregular coefficients, Small noise asymptotic expansions",

author = "Benjamin Gess and Zhengyan Wu and Rangrang Zhang",

note = "Publisher Copyright: {\textcopyright} 2025 The Authors",

year = "2026",

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doi = "10.1016/j.spa.2025.104847",

language = "English",

volume = "193",

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T1 - Higher order fluctuation expansions for nonlinear stochastic heat equations in singular limits

AU - Gess, Benjamin

AU - Wu, Zhengyan

AU - Zhang, Rangrang

PY - 2026/3

Y1 - 2026/3

N2 - 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.

AB - 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.

KW - Conservative SPDEs

KW - Edgeworth expansion

KW - Higher order fluctuation

KW - Irregular coefficients

KW - Small noise asymptotic expansions

UR - https://www.scopus.com/pages/publications/105025004431

U2 - 10.1016/j.spa.2025.104847

DO - 10.1016/j.spa.2025.104847

M3 - Article

AN - SCOPUS:105025004431

SN - 0304-4149

VL - 193

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

M1 - 104847

ER -

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

Abstract

Keywords

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