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Moment Constants for Brownian Affine Approximation — arXiv:2609.08068

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.08068
License (as archived): CC0-1.0
Archived: 2026-10-16T14:32:38.333Z
SHA-256 of the archived text: 94fbe9292d412af2e297808f4a92ee540412fb926f75b9f50af4c6baa379a8c5
Stable URL of this page: https://metraipolis.com/documento/dc_7ee548360900

How to cite

Moment Constants for Brownian Affine Approximation — arXiv:2609.08068 — arXiv (en), https://arxiv.org/abs/2609.08068 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7ee548360900 (Metraipolis archive dc_7ee548360900, sha256 94fbe9292d412af2e297808f4a92ee540412fb926f75b9f50af4c6baa379a8c5)

BibTeX

@misc{dc7ee548360900,
  title = {Moment Constants for Brownian Affine Approximation — arXiv:2609.08068},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.08068},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7ee548360900; sha256 94fbe9292d412af2e297808f4a92ee540412fb926f75b9f50af4c6baa379a8c5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.08068. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $\zeta(2j+1)/\pi^{2j}$, $1\le j\le4$; the means are $40\zeta(3)/\pi^2-4/3$ and $21\zeta(3)/\pi^2$, 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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.08068 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T14:09:59.788Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).