[1]汪园芳,吴群英.非平稳高斯序列最大值与部分和的几乎处处中心极限定理[J].华侨大学学报(自然科学版),2015,36(1):116-120.[doi:10.11830/ISSN.1000-5013.2015.01.0116]
　WANG Yuan-fang,WU Qun-ying.Almost Sure Central Limit Theorem for Maxima and Partial Sums of Non-Stationary Gaussian Sequence[J].Journal of Huaqiao University(Natural Science),2015,36(1):116-120.[doi:10.11830/ISSN.1000-5013.2015.01.0116]
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非平稳高斯序列最大值与部分和的几乎处处中心极限定理()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第36卷
期数:
2015年第1期
页码:
116-120
栏目:
出版日期:
2015-01-20

文章信息/Info

Title:
Almost Sure Central Limit Theorem for Maxima and Partial Sums of Non-Stationary Gaussian Sequence
文章编号:
1000-5013(2015)01-0116-05
作者:
汪园芳;  吴群英
桂林理工大学 理学院, 广西 桂林 541004
Author(s):
WANG Yuan-fang;  WU Qun-ying
College of Science, Guilin University of Technology, Guilin 541004, China
关键词:
几乎处处中心极限定理;  最大值与部分和;  非平稳高斯序列;  收敛性
Keywords:
almost sure central limit theorem;  maxima and partial sums;  non-stationary Gaussian sequence;  convergence
分类号:
O22.4
DOI:
10.11830/ISSN.1000-5013.2015.01.0116
文献标志码:
A
摘要:
假设{Xn,n≥1}为标准化非平稳高斯序列,在协方差和常数列{un,i,1≤i≤n,n≥1}满足适当的条件下,获得了最大值与部分和的几乎处处中心极限定理,并优化了臧庆佩所获得的结果.
Abstract:
Suppose {Xn,n≥1} is a standardized non-stationary Gaussian sequence. The almost sure central limit theorem for maxima and partial sums is derived under some conditions on the covariance function and the constant sequence {un,i,1≤i≤n,n≥1}. The result generalizes the one obtained by Zang Qing-pei.

参考文献/References:

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[3] FAHRNER I,STADTMULLER U.On almost sure central max-limit theorems[J].Statist Probab Lett,1998,37(3):229-236.
[4] CHENG Shi-hong,PENG Liang,QI Yong-cheng.Almost sure convergence in extreme value theory[J].Math Nachr,1998,190(1):43-50.
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[6] DUDZINSKI M.The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences[J].Statist Probab Lett,2008,78(4):347-357.
[7] ZANG Qing-pei.Almost sure central limit theorem for a non-stationary sequence[J].J Inequ Appl,2010,10:1155-1163.
[8] WU Qun-yin.Almost sure central limit theory for products of sums of partial sums[J].Appl Math J Chinese Univ,2012,27(2):169-180.
[9] LEADBETTER M R,LINDGREN G,ROOTZEN H.Extremes and related properties of random sequences and processes[M].New York:Springer,1983:84-85.
[10] 吴群英.混合序列的概率极限理论[M].北京:科学出版社,2006:89-90.

备注/Memo

备注/Memo:
收稿日期: 2014-05-21
通信作者: 吴群英(1961-),女,教授,博士,主要从事极限理论的研究.E-mail:wqy666@glut.edu.cn.
基金项目: 国家自然科学基金资助项目(11361019); 广西省研究生教育创新计划资助项目(YCSZ2014158)
更新日期/Last Update: 2015-01-20