A Note on the Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Partial Sums of Certain Stationary Gaussian Sequences

• 作者: Qunying Wu Yuanfang Wang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: ALMOST Sure Central Limit Theorem STATIONARY GAUSSIAN Sequence Slowly VARYING Functions at INFINITY
• 年，卷（期）: 2014,（10）
• 页码范围: 1598-1608
• 页数: 11页
• 分类号: O21

摘要

Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.