{
  "abstract": "We establish a functional central limit theorem (CLT) for fluctuations of time-integrated functionals of empirical measures arising from interacting McKean--Vlasov particle systems. Our framework allows for coefficients with unbounded spatial growth and dependence on arbitrarily high-order moments of the measure variable, extending the scope of the existing fluctuation theory. The proof uses a novel approach combining linear functional differentiation with new well-posedness results and estimates for perturbed backward parabolic equations in polynomially weighted Schauder spaces, yielding a martingale-type representation of the fluctuations with an asymptotically negligible remainder. The limiting process is shown to be centred Gaussian with an explicit covariance structure. As a statistical application, we derive the asymptotic theory underlying hypothesis tests for both the temporal constancy of population characteristics and parametric restrictions on the drift coefficient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34347",
  "author_total": 2,
  "authors": [
    {
      "name": "Mark Podolskij"
    },
    {
      "name": "Fabrice Wunderlich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1xj4mhaxdf5n8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34347",
  "fulltext_url": null,
  "id": "1xj4mhaxdf5n8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34347",
  "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.TH"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7223812664",
  "pdf_url": "https://arxiv.org/pdf/2610.34347",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1xj4mhaxdf5n8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34347",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34347"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A functional central limit theorem for particle systems under polynomial growth conditions, with applications to statistics",
  "title_text": "A functional central limit theorem for particle systems under polynomial growth conditions, with applications to statistics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/1xj4mhaxdf5n8",
  "venue": "arXiv",
  "versions": []
}