{
  "abstract": "We study the stochastic heat equation on a bounded interval with zero Dirichlet boundary conditions, driven by symmetric $α$-stable space--time Lévy white noise, where $1<α<2$. Both the drift and noise coefficients are continuous and have at most linear growth. For bounded deterministic initial data and every $r>1/2$, we construct a weak solution with càdlàg paths in the negative Sobolev space $\\mathbb{H}_{-r}$. We also construct a predictable mild solution on the same stochastic basis and with the same noise. At each fixed deterministic time, this mild solution is a density of the distribution-valued weak solution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04895",
  "author_total": 1,
  "authors": [
    {
      "name": "Juan J. Jiménez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dbgbbb2s33tg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04895",
  "fulltext_url": null,
  "id": "3dbgbbb2s33tg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04895",
  "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",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7220714708",
  "pdf_url": "https://arxiv.org/pdf/2610.04895",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3dbgbbb2s33tg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04895",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04895"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stochastic heat equations with non-Lipschitz coefficients driven by symmetric $α$-stable Lévy white noise",
  "title_text": "Stochastic heat equations with non-Lipschitz coefficients driven by symmetric α-stable Lévy white noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/3dbgbbb2s33tg",
  "venue": "arXiv",
  "versions": []
}