重尾随机变量和的大偏差

数学季刊 ›› 2007, Vol. 22 ›› Issue (2): 282-289.

重尾随机变量和的大偏差

Department of Mathematics Anhui University,Department of Mathematics Anhui University,,Hefei 230039 China,Hefei 230039 China

收稿日期:2005-01-10 出版日期:2007-06-30 发布日期:2023-11-06
作者简介:GUO Xiao-yan(1979-),female,native of Xuancheng,Anhui,M.S.D.,engages in applied prob- ability;KONG Fan-chao(1943-),male,native of Hefei,Anhui,a profeesor of Anhui University,engages in probability theory and its applications.

Large Deviations for Sums of Heavy-tailed Random Variables

Department of Mathematics Anhui University,Department of Mathematics Anhui University,,Hefei 230039 China,Hefei 230039 China

Received:2005-01-10 Online:2007-06-30 Published:2023-11-06
About author:GUO Xiao-yan(1979-),female,native of Xuancheng,Anhui,M.S.D.,engages in applied prob- ability;KONG Fan-chao(1943-),male,native of Hefei,Anhui,a profeesor of Anhui University,engages in probability theory and its applications.

摘要/Abstract

摘要： This paper is a further investigation of large deviations for sums of random variables Sn=sum form i=1 to n Xi and S(t)=sum form i=1 to N(t) Xi,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.

关键词: large deviation;heavy-tailed distribution;strongly subexponential distribution, lognormal distribution

Abstract: This paper is a further investigation of large deviations for sums of random variables Sn=sum form i=1 to n Xi and S(t)=sum form i=1 to N(t) Xi,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.

Key words: large deviation;heavy-tailed distribution;strongly subexponential distribution, lognormal distribution

中图分类号:

O211.5

郭晓燕, 孔繁超. 重尾随机变量和的大偏差[J]. 数学季刊, 2007, 22(2): 282-289.

GUO Xiao-yan, KONG Fan-chao. Large Deviations for Sums of Heavy-tailed Random Variables [J]. Chinese Quarterly Journal of Mathematics, 2007, 22(2): 282-289.

[1]	李克典. 锥度量空间的完备性[J]. 数学季刊, 2013, 28(4): 565-572.
[2]	李伟平, 戈文旭, 王天泽. 混合幂次为2和4的整数变量非线性型的整数部分[J]. 数学季刊, 2013, 28(3): 317-322.
[3]	商宇, 汪立民. 关于4-循环半群的一些子半群-Ⅱ[J]. 数学季刊, 2013, 28(3): 390-396.
[4]	杨纪华, 刘媚. 具时滞人机系统的稳定性与分支分析[J]. 数学季刊, 2012, 27(2): 196-203.
[5]	叶绪国, 杜雪樵. 对于金融资产漂移函数估计的双域组合方法[J]. 数学季刊, 2011, 26(2): 190-195.
[6]	李守伟, 祝东进. 随机环境中马氏链的首达分布矩[J]. 数学季刊, 2011, 26(1): 51-55.
[7]	刘玉记 . 具有p-Laplacian算子的二阶微分方程Picard边值问题[J]. 数学季刊, 2011, 26(1): 77-84.
[8]	王勇, 张良云, 蔡之敏 . 模余代数的结构定理[J]. 数学季刊, 2011, 26(1): 85-92.
[9]	彭婷婷, 郭小江. 因子拟适当半群[J]. 数学季刊, 2011, 26(1): 93-99.
[10]	吴明忠. 以幂零李代数Rn为幂零根基的可解李代数[J]. 数学季刊, 2011, 26(1): 100-107.
[11]	谭成良, 吴群英, 何燕梅. ρ^-_-混合序列部分和最大值的一些不等式和强大数律的收敛速度[J]. 数学季刊, 2011, 26(1): 114-119.
[12]	王金凤, 刘洋, 李宏. 粘弹性波动方程的H¹-Galerkin混合有限元方法误差估计[J]. 数学季刊, 2011, 26(1): 131-137.
[13]	梁菊花, 任立顺, 赵志良. 一类带有三维核的多点边值问题解的存在性[J]. 数学季刊, 2011, 26(1): 138-143.
[14]	周宏宪, 张燕. 一类Z₂-等变扰动的三次哈密顿系统极限环的个数与分布[J]. 数学季刊, 2011, 26(1): 144-151.
[15]	汪忠志 . 关于任意随机序列的一个强大数定理[J]. 数学季刊, 2010, 25(4): 475-480.