{
  "abstract": "In this article, we study the second-order fluctuation of the solutions of one-dimensional polynomial stochastic partial differential equations (SPDEs) of the form \\begin{equation*} (\\partial_t - Δ) Φ_{\\varepsilon} = -P(Φ_{\\varepsilon}) + ξ_{\\varepsilon}, \\end{equation*} where $P$ is a polynomial of degree greater than or equal to $2$, $ξ_\\varepsilon$ is the white-noise after being convoluted (in space) by the heat kernel $K_\\varepsilon = e^{\\varepsilon Δ}$. More precisely, taking advantage of the local solutions of pointwise well-posedness of limits $Φ= \\lim_{\\varepsilon \\to 0}Φ_{\\varepsilon}$, we characterise the limit of $Φ^{err}=\\lim_{\\varepsilon \\to 0} \\varepsilon^{-1}(Φ_{\\varepsilon}-Φ)$ as the solution of a more irregular stochastic partial differential equation. This is performed by applying the Da Prato--Debussche decomposition in the non-linear equation and characterising the limit of each of the terms. We also discuss possible characterisations of second-order fluctuations performed for higher-dimensional SPDEs in the weakly-coupled regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09540",
  "author_total": 3,
  "authors": [
    {
      "name": "Eldon Barros"
    },
    {
      "name": "Leandro Chiarini"
    },
    {
      "name": "Milton Jara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hev0ze4gakxd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09540",
  "fulltext_url": null,
  "id": "4hev0ze4gakxd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09540",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212181225",
  "pdf_url": "https://arxiv.org/pdf/2609.09540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hev0ze4gakxd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09540"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Second-order fields for stochastic partial differential equations",
  "title_text": "Second-order fields for stochastic partial differential equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/4hev0ze4gakxd",
  "venue": "arXiv",
  "versions": []
}