{
  "abstract": "We study McKean-Vlasov equations driven by an isotropic $2s$-stable Lévy noise, $s\\in(0,1)$, whose solutions may have no finite mean, with coefficients that are Lipschitz with respect to a bounded Wasserstein-type distance. When the jump noise is additive, we prove strong well-posedness for every initial law and every $s$, without any moment assumption, and propagation of chaos at the rate $N^{-1/2}$ for kernel interactions. When the size of the jumps depends on the law, we prove the same results for $s>1/2$, and we show by an example that uniqueness fails for every $s<1/2$. The value $s=1/2$ thus separates well-posedness from non-uniqueness; the critical case itself remains open. These results answer, for stable noise, the question of uniqueness without moments raised by Jourdain, Méléard and Woyczyński and by Cavallazzi.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02859",
  "author_total": 1,
  "authors": [
    {
      "name": "Houssine El Jeddaoui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16ax0wv5jtw5c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02859",
  "fulltext_url": null,
  "id": "16ax0wv5jtw5c",
  "issns": [],
  "landing_url": "https://hal.science/hal-05847009v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-pr"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05847009/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16ax0wv5jtw5c.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:44Z",
      "native_id": "hal-05847009",
      "source": "hal",
      "url": "https://hal.science/hal-05847009v1"
    },
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02859",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02859"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "McKean-Vlasov flights without moments: well-posedness, propagation of chaos and a critical threshold for law-dependent jumps",
  "title_text": "McKean-Vlasov flights without moments: well-posedness, propagation of chaos and a critical threshold for law-dependent jumps",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/16ax0wv5jtw5c",
  "venue": "HAL",
  "versions": []
}