{
  "abstract": "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 $(Ω,\\mathscr{H},\\widehat{\\mathbb E})$, 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Science in China-Mathematics (Chinese), 2026",
  "arxiv": "2608.30848",
  "author_total": 2,
  "authors": [
    {
      "name": "Li-Xin Zhang"
    },
    {
      "name": "Yongsheng Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dp8fz0qr9tc55.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30848",
  "fulltext_url": null,
  "id": "dp8fz0qr9tc55",
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  "landing_url": "https://arxiv.org/abs/2608.30848",
  "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"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.30848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dp8fz0qr9tc55.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2608.30848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30848"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Limit Laws of the Iterated Logarithm Under Sub-linear Expectations",
  "title_text": "Limit Laws of the Iterated Logarithm Under Sub-linear Expectations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/dp8fz0qr9tc55",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1360/ssm-2026-0178",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}