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Limit Laws of the Iterated Logarithm Under Sub-linear Expectations — arXiv:2608.30848

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.30848
License (as archived): CC0-1.0
Archived: 2026-10-17T09:10:09.774Z
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Limit Laws of the Iterated Logarithm Under Sub-linear Expectations — arXiv:2608.30848 — arXiv (en), https://arxiv.org/abs/2608.30848 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bcab022ca470 (Metraipolis archive dc_bcab022ca470, sha256 51062326849a1ca615404d196008ed60f7d2cd5b692e8bd518eb2ac21a72863b)

BibTeX

@misc{dcbcab022ca470,
  title = {Limit Laws of the Iterated Logarithm Under Sub-linear Expectations — arXiv:2608.30848},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.30848},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bcab022ca470; sha256 51062326849a1ca615404d196008ed60f7d2cd5b692e8bd518eb2ac21a72863b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.30848. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $\{Y_n; n\ge 1\}$ be a sequence of independent and identically distributed random variables with mean zero in Peng's framework of the sub-linear expectation space $(\Omega,\mathscr{H},\widehat{\mathbb E})$, and $S_n=\sum_{i=1}^nY_i$. In this paper, we establish a limit law of \begin{align*}\lim_{n\to \infty}\max_{k\le n}\frac{S_k}{\sqrt{2k \log\log n}}. \end{align*} Different from the result obtained by Chen (2015) in which the limit is a constant, it is shown that under the upper capacity the limit may be prescribed as a given function of $Y_1,Y_2,\ldots$, taking values in the standard deviation interval. As a result, it is also shown that the set of limit points in the compact law of the iterated logarithm can be a symmetric random interval. This paper (Chinese version) has been submitted to Special Issue of Science in China-Mathematics in Celebration of Professor Peng Shige's 80th Birthday. In Theorem 2.2 of the original paper, an additional condition (2.6) is needed.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2608.30848 — 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 2026-10-17T08:40:49.534Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).