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| 非平稳高斯序列最大值的几乎处处中心极限定理 | |
| 引用本文： | 胡爱平,伍度志,彭作祥,刘瑞华,汪益川.非平稳高斯序列最大值的几乎处处中心极限定理[J].后勤工程学院学报,2011,27(3):82-86. |
| 作者姓名： | 胡爱平 伍度志 彭作祥 刘瑞华 汪益川 |
| 作者单位： | 1. 重庆理工大学数学与统计学院,重庆,400054 2. 后勤工程学院基础部,重庆,401311 3. 西南大学数学与统计学院,重庆,400715 4. 后勤工程学院科研部,重庆,401311 |
| 基金项目： | 重庆市教育委员会科学技术研究资助项目 |
| 摘 要： | 在较弱的条件下,研究了一类非平稳高斯序列的几乎处处中心极限定理.设{Xa,n≥1}为一非平稳高斯序列,记其协方差为rij=Cov(Xi,Xj).假设该序列满足如下条件:对充分大的n,若存在0<α<1当|i-j|>nα时,rijlog|j-i|(l0glog|j-i|)1+ε一致有界.在这一条件下,通过利用概率极限理论,... |
| 关 键 词： | 几乎处处中心极限定理 对数平均 非平稳高斯序列 |
Almost Sure Central Limit Theorem for the Maxima of Non-stationary Gaussian Sequence |
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| HU Ai-ping,WU Du-zhi,PENG Zuo-xiang,LIU Rui-hua,WANG Yi-chuan.Almost Sure Central Limit Theorem for the Maxima of Non-stationary Gaussian Sequence[J].Journal of Logistical Engineering University,2011,27(3):82-86. | |
| Authors: | HU Ai-ping WU Du-zhi PENG Zuo-xiang LIU Rui-hua WANG Yi-chuan |
| Institution: | 1.School of Mathematics and Statistics,Chongqing University of Technology,Chongqing 400054,China;2.Dept.of Foundation Studies,LEU,Chongqing 401311,China;3.School of Mathematics and Finance,Southwest University,Chongqing 400715,China;4.Dept.of Science & Research,LEU,Chongqing 401311,China) |
| Abstract: | The almost sure central limit theorem for the maxima of non-stationary Gaussian sequence is studied under weak qualification.Let{Xn,n≥1} be a sequence of non-stationary Gaussian sequence,with covariance rij=Cov(Xi,Xj),and suppose there exists a constant 0<α<1,for positive integer n large enough,such that as |i-j|>nα,rijlog|j-i|(loglog|j-i|)1+ε is uniformly bounded.Therefore,the almost sure central limit theorem for the maxima of non-stationary Gaussian sequence is derived,which generalizes the result presented by Khurelbaatar Gonchigdanzan. |
| Keywords: | almost sure central limit theorem logarithmic average non-stationary Gaussian sequence |
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