English

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

Probability 2024-06-27 v1 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.2406.17892,
  title  = {Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits},
  author = {Benjamin Gess and Zhengyan Wu and Rangrang Zhang},
  journal= {arXiv preprint arXiv:2406.17892},
  year   = {2024}
}

Comments

51 pages

R2 v1 2026-06-28T17:19:12.385Z