{
  "abstract": "We evaluate moment constants for the times during which Brownian motion admits uniform approximation by an unrestricted affine function or by a line through the origin. The first four moments are rational linear combinations of $1$ and $ζ(2j+1)/π^{2j}$, $1\\le j\\le4$; the means are $40ζ(3)/π^2-4/3$ and $21ζ(3)/π^2$, respectively. Slope integration and a common contour argument give the unrestricted moments, while time inversion relates the anchored law to the reciprocal of Kingman's absorption time. For both models we also give exponential-integral series for the standardized absolute third central moments, with explicit truncation bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08068",
  "author_total": 1,
  "authors": [
    {
      "name": "Yue Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3tn6pvtwgtn57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08068",
  "fulltext_url": null,
  "id": "3tn6pvtwgtn57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08068",
  "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",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7211990499",
  "pdf_url": "https://arxiv.org/pdf/2609.08068",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3tn6pvtwgtn57.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08068",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08068"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Moment Constants for Brownian Affine Approximation",
  "title_text": "Moment Constants for Brownian Affine Approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/3tn6pvtwgtn57",
  "venue": "arXiv",
  "versions": []
}