{
  "abstract": "We study density regularity and optimal Gaussian approximation for complex multiple Wiener-Itô integrals. We first give a kernel criterion for absolute continuity and derive explicit formulas for the density and its derivatives, together with finite-order Sobolev estimates. Our main quantitative result shows that the sum of an intrinsic non-Gaussian term and the covariance mismatch gives the optimal rate simultaneously in every fixed Sobolev norm and in total variation, Kolmogorov and $1$-Wasserstein distances. The intrinsic term is determined by two complex third-order moments and the complex fourth-moment defect, and is equivalently described by complex kernel contractions. No additional Malliavin non-degeneracy assumption is imposed in these asymptotic results. As an application, we obtain explicit optimal rates for the normalized numerator in the least-squares estimator of a complex fractional Ornstein--Uhlenbeck process.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04532",
  "author_total": 3,
  "authors": [
    {
      "name": "Huiping Chen"
    },
    {
      "name": "Yong Chen"
    },
    {
      "name": "Yong Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ggw2vmcbrc2z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04532",
  "fulltext_url": null,
  "id": "8ggw2vmcbrc2z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04532",
  "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"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7220674621",
  "pdf_url": "https://arxiv.org/pdf/2610.04532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ggw2vmcbrc2z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04532"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Optimal Gaussian approximation for complex Wiener-Itô integrals",
  "title_text": "Optimal Gaussian approximation for complex Wiener-Itô integrals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8ggw2vmcbrc2z",
  "venue": "arXiv",
  "versions": []
}