{
  "abstract": "We show that uniqueness may fail for one-dimensional McKean--Vlasov stochastic differential equations with Hölder continuous diffusion coefficients. More precisely, for every \\(α\\in(1/2,1)\\), we construct an equation with a diffusion coefficient that is \\(α\\)-Hölder continuous in the state variable, Lipschitz continuous in the measure variable, and of linear growth, for which uniqueness in law and pathwise uniqueness fail. The construction relies on a spreading estimate together with a Schauder fixed-point argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15017",
  "author_total": 3,
  "authors": [
    {
      "name": "Martin Bergerhausen"
    },
    {
      "name": "Paul Nikolaev"
    },
    {
      "name": "David J. Prömel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bymrpj83g0ts.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15017",
  "fulltext_url": null,
  "id": "7bymrpj83g0ts",
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  "landing_url": "https://arxiv.org/abs/2610.15017",
  "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.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7221776765",
  "pdf_url": "https://arxiv.org/pdf/2610.15017",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bymrpj83g0ts.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15017",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15017"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Non-uniqueness for McKean--Vlasov SDEs with Hölder diffusion coefficients",
  "title_text": "Non-uniqueness for McKean--Vlasov SDEs with Hölder diffusion coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7bymrpj83g0ts",
  "venue": "arXiv",
  "versions": []
}