{
  "abstract": "The present research is devoted to the nonparametric estimation of a density-dependent drift coefficient in a multivariate McKean--Vlasov diffusion from independent observations at a common time, as well as the stationary density. Under certain assumptions on the (known) potential, we reduce the problem to the one-dimensional one and construct a sieve maximum-likelihood estimator based on sparse ReQU neural networks subject to structural and Hölder constraints. Using the endpoint-adapted graded approximation, we achieve the rate of $\\left(b_n\\log n/n\\right)^{2(β+1)/(2β+3)}$ for the Kullback-Leibler divergence between the true and estimated stationary densities, with $b_n$ being at most a logarithmic factor. Similarly, it is shown that the constructed estimator for the drift coefficient converges to the true one at the rate of $\\left(b_n\\log n/n\\right)^{β/(2β+3)}$ in the $L^2$-metric. A matching Assouad lower bound proves minimax optimality of this bound up to logarithmic factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01166",
  "author_total": 2,
  "authors": [
    {
      "name": "Denis Belomestny"
    },
    {
      "name": "Ekaterina Morozova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fh6fvx179zhzd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01166",
  "fulltext_url": null,
  "id": "fh6fvx179zhzd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01166",
  "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"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7206157887",
  "pdf_url": "https://arxiv.org/pdf/2609.01166",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fh6fvx179zhzd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01166",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01166"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Nonparametric inference for density-dependent McKean--Vlasov diffusions",
  "title_text": "Nonparametric inference for density-dependent McKean--Vlasov diffusions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:10Z",
  "url": "https://research.draconitic.com/paper/fh6fvx179zhzd",
  "venue": "arXiv",
  "versions": []
}