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Uniform transport processes and the Brownian sheet:the one-parameter rate of convergence is preserved — arXiv:2610.23347

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.23347
License (as archived): CC0-1.0
Archived: 2026-10-19T09:38:04.210Z
SHA-256 of the archived text: b07b939e7c32d7b49be092ebf4bb92b9dc9142e23bb44a31e5ba96b4d60f5179
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Uniform transport processes and the Brownian sheet:the one-parameter rate of convergence is preserved — arXiv:2610.23347 — arXiv (en), https://arxiv.org/abs/2610.23347 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2ced7dacabba (Metraipolis archive dc_2ced7dacabba, sha256 b07b939e7c32d7b49be092ebf4bb92b9dc9142e23bb44a31e5ba96b4d60f5179)

BibTeX

@misc{dc2ced7dacabba,
  title = {Uniform transport processes and the Brownian sheet:the one-parameter rate of convergence is preserved — arXiv:2610.23347},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.23347},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2ced7dacabba; sha256 b07b939e7c32d7b49be092ebf4bb92b9dc9142e23bb44a31e5ba96b4d60f5179},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.23347. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In~\cite{BFR} we constructed processes $W_n$, built from a family of independent standard Poisson processes, that converge almost surely to the Brownian sheet uniformly on $[0,1]^2$, and in~\cite{Rov} we proved that $P(\max_{[0,1]^2}|W_n-W|>\alpha n^{-\beta})=o(n^{-q})$ for every $\beta<\lambda/2$, where $\lambda\in(0,\tfrac{1}{5})$ is the parameter of the construction; this gives rates $n^{-\beta}$ with $\beta<\tfrac{1}{10}$. In this paper, we show that the same construction, with $\lambda\geq 1$, satisfies \[ P\!\left(\max_{(s,t)\in[0,1]^2} |W_n(s,t)-W(s,t)| > \alpha\, n^{-1/2}(\log n)^3\right) = o(n^{-q}) \quad\text{for every }q>0, \] which is the one-parameter rate of Gorostiza and Griego~\cite{GG} up to a factor $(\log n)^{1/2}$. In particular the restriction $\lambda<\tfrac{1}{5}$ is not needed.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.23347 — 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 2026-10-19T09:34:14.701Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).