华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (4): 62-68.

• 应用数学与基础数学 • 上一篇    下一篇

重尾分布类$\mathcal{D}\cap\mathcal{L}$中负相伴随机变量和的精确大偏差

汪世界$^{1, 2}$, 王文胜$^1$

  

  1. 1. 华东师范大学~~金融统计学院, 上海 200241; 2. 安徽大学~~数学科学学院, 合肥 230039
  • 收稿日期:2008-07-02 修回日期:2008-12-06 出版日期:2009-07-25 发布日期:2009-07-25
  • 通讯作者: 汪世界

Precise large deviation for sums of negatively associated \\[5pt]heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L

WANG Shi-jie $^{1, 2}$, WANG Wen-sheng$^2   

  1. 1. {\it School of Finance and Statistics, East China Normal University, Shanghai} 200241, {\it China
  • Received:2008-07-02 Revised:2008-12-06 Online:2009-07-25 Published:2009-07-25
  • Contact: WANG Shi-jie

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摘要： 利用重尾分布类$\mathcal{D}\cap\mathcal{L}$性质的刻画，得到了重尾分布类$\mathcal{D}\cap\mathcal{L}$中负相伴重尾随机变量和(随机和与非随机和)的精确大偏差，
而重尾分布类$\mathcal{D}\cap\mathcal{L}$是严格包含$\mathcal{C}$的，从而首次将现有的精确大偏差结果推广到更大的重尾分布子类上

关键词: 负相伴, 一致变化尾, 控制变化尾, 长尾, 精确大偏差, 负相伴, 一致变化尾, 控制变化尾, 长尾, 精确大偏差

Abstract: By using the characterization of heavy-tailed random variables in
$\mathcal{D}\cap\mathcal{L}$, precise large
deviations for sums (nonrandom sums and random sums) of negatively associated
heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L}$ were obtained, where the
subclass $\mathcal{D}\cap\mathcal{L}$ strictly contains $\mathcal{C}$. Therefore, it
firstly extends some existed precise large deviation results to some larger subclasses
of heavy tailed distributions.

Key words: consistently varying tail, dominately varying tail, long tail, precise large deviation, negatively association, consistently varying tail, dominately varying tail, long tail, precise large deviation

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