{
  "abstract": "We prove weak existence and uniqueness in law of $[0,1]$-valued solutions for a class of scalar stochastic heat equations with measurable drifts $b : [0,1] \\to \\mathbb{R}$, driven by Wright--Fisher noise. The only assumptions we require on the drift are Borel-measurability, and the one-way inequalities $-Cu\\leq b(u)\\leq C(1-u)$ for some $C<\\infty$, compatible with the necessary condition $b(1)\\leq 0\\leq b(0)$. These are vastly more general conditions than were previously available. Our proof relies on a stochastic duality between the solution of the stochastic heat equation, and a voting scheme running along the graph of a branching-coalescing particle system, generalising the class of drifts for which a dual process is available. Our results and their proof put the regularisation-by-noise result of Barnes, Mytnik and Sun, and its explanation, on a much more general footing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23518",
  "author_total": 2,
  "authors": [
    {
      "name": "Jere Koskela"
    },
    {
      "name": "Oliver Tough"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5rbftm7jdt79.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23518",
  "fulltext_url": null,
  "id": "b5rbftm7jdt79",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23518",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214025092",
  "pdf_url": "https://arxiv.org/pdf/2609.23518",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5rbftm7jdt79.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23518",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23518"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Well-posedness for Wright--Fisher SPDEs with measurable drift",
  "title_text": "Well-posedness for Wright--Fisher SPDEs with measurable drift",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/b5rbftm7jdt79",
  "venue": "arXiv",
  "versions": []
}