{
  "abstract": "These notes were prepared for a series of lectures delivered at the 43rd Finnish Summer School on Probability and Statistics, held in Lammi, Finland, from May 26 to 30, 2025. They provide an introduction to McKean-Vlasov stochastic differential equations and their connections with non-linear Fokker-Planck equations and mean-field interacting particle systems. Particular attention is devoted to density-dependent equations and to kinetic-type models with degenerate noise. For the latter, we introduce the underlying non-Euclidean geometry and the associated anisotropic and intrinsic Hölder spaces, and present well-posedness and regularity results based on Schauder estimates and superposition principles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30493",
  "author_total": 1,
  "authors": [
    {
      "name": "Stefano Pagliarani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fjytf3jympms.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30493",
  "fulltext_url": null,
  "id": "8fjytf3jympms",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30493",
  "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.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7204943468",
  "pdf_url": "https://arxiv.org/pdf/2608.30493",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fjytf3jympms.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30493"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models",
  "title_text": "McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/8fjytf3jympms",
  "venue": "arXiv",
  "versions": []
}