{
  "abstract": "We analyze explicit tamed Euler approximations for weakly interacting particle systems and McKean--Vlasov diffusions with additive noise and polynomially weighted locally Hölder, possibly superlinear drift.Under dissipativity at infinity and suitable stability assumptions, we establish time-uniform $W_1$ bounds by reflection coupling, separating relaxation, time-discretization, and finite-particle errors.For small step sizes, we prove existence and uniqueness of numerical invariant laws and bound their error relative to the continuous-time particle invariant law uniformly in $N$ in a normalized joint $W_1$ distance. We further bound the error of the one-particle numerical invariant marginal relative to the McKean--Vlasov invariant law by $O(θ^{\\min\\{α,β/2\\}}+N^{-1/2})$, where $θ$ is the step size, $N$ the particle number, $α\\in(0,1/2]$ the taming exponent, and $β\\in(0,1]$ the Hölder exponent. Analytical examples illustrate the framework for smooth and non-Lipschitz drifts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29314",
  "author_total": 4,
  "authors": [
    {
      "name": "Lingyan Cheng"
    },
    {
      "name": "Ruinan Li"
    },
    {
      "name": "Shiyu Liu"
    },
    {
      "name": "Wei Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/855hxkx1ncq29.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29314",
  "fulltext_url": null,
  "id": "855hxkx1ncq29",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29314",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7223203426",
  "pdf_url": "https://arxiv.org/pdf/2610.29314",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/855hxkx1ncq29.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29314",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29314"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Tamed Euler Approximation of Invariant Measures for Weakly Interacting Particle Systems and McKean--Vlasov Equations",
  "title_text": "Tamed Euler Approximation of Invariant Measures for Weakly Interacting Particle Systems and McKean--Vlasov Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/855hxkx1ncq29",
  "venue": "arXiv",
  "versions": []
}