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

• Authors: Benjamin Gess, Zhengyan Wu, Rangrang Zhang
• First public date: 2024-06-25
• arXiv: 2406.17892
• Preprint year: 2024
• Status: Published
• Publication type: Journal article
• Publication year: 2026
• Journal: Stochastic processes and their applications, 193 (2026), p. 104847
• DOI: 10.1016/j.spa.2025.104847

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.

Associated SAiS members

• Benjamin Gess

Associated projects

• FluCo

Research areas

• SPDEs
• Non-equilibrium Statistical Mechanics, Interacting Particle Systems and Fluctuating Hydrodynamics

BibTeX

@article{arxiv240617892,
  title = {Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits},
  author = {Benjamin Gess and Zhengyan Wu and Rangrang Zhang},
  year = {2026},
  journal = {Stochastic processes and their applications, 193 (2026), p. 104847},
  doi = {10.1016/j.spa.2025.104847},
  eprint = {2406.17892},
  archivePrefix = {arXiv},
  primaryClass = {math.PR}
}