发表机构
Zhejiang Gongshang University; Zhejiang University; University of Chinese Academy of Sciences（浙江工商大学; 浙江大学; 中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Peng的次线性期望空间框架下，建立了一类重对数极限律，其极限可为随机区间，相关成果已提交至《中国科学-数学》彭实戈教授八十寿辰专刊。
AI 中文摘要
设{Y_n; n≥1}是Peng的次线性期望空间(Ω,ℋ,Ê)中均值为零的独立同分布随机变量序列，记S_n=∑_{i=1}^nY_i。本文建立了极限lim_{n→∞}max_{k≤n}S_k/√(2k log log n)的极限律。与Chen(2015)得到的极限为常数的结果不同，本文证明了在上容量下，该极限可被指定为Y₁,Y₂,…的给定函数，取值于标准差区间。由此还证明了重对数律紧极限点集可为对称随机区间。本文的中文版已提交至《中国科学-数学》专刊，用以庆贺彭实戈教授八十寿辰。
英文摘要
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.
Comments24 pages
Journal refScience in China-Mathematics (Chinese), 2026
