一个不满足中心极限定理的严平稳相伴随机序列

广西师范大学学报（自然科学版） ›› 2010, Vol. 28 ›› Issue (3): 20-23.

一个不满足中心极限定理的严平稳相伴随机序列

贾保华

宁夏大学数学计算机学院,宁夏银川750021

收稿日期:2010-03-10 出版日期:2010-09-20 发布日期:2023-02-06
通讯作者: 贾保华(1954—),男,宁夏平罗人,宁夏大学副教授。E-mail:jia.401@163.com
基金资助:
国家自然科学基金资助项目(10502026);宁夏自然科学基金资助项目(NZ1050);宁夏大学科研基金资助项目(ZR200817;ndzr09-27)

A Strictly Stationary Associated Random Sequence Which Unsatisfythe Central Limit Theorem

JIA Bao-hua

School of Mathematics and Computer Science,Ningxia University,Yinchuan Ningxia 750021,China

Received:2010-03-10 Online:2010-09-20 Published:2023-02-06

摘要/Abstract

摘要： 构造了一个不满足中心极限定理且部分和的方差按照一定规则变化的严平稳相伴随机序列的例子,这个结论推广了N.Herrndorf著名的例子并且说明了经典纽曼定理的最优性条件。

关键词: 相伴随机序列, 中心极限定理, 平稳性, 缓变函数

Abstract: An example of a strictly stationary associated randomsequence which does not satisfy the central limit theorem and whose partial sums' variance grows in a defined regular way is constructed.The well-known example of N.Herrndorf is generalized and the optimality of conditions in the classical Newman's theorem is shown.

Key words: associated random sequences, central limit theorem, stationarity, slowly varying functions

中图分类号:

O211.4

贾保华. 一个不满足中心极限定理的严平稳相伴随机序列[J]. 广西师范大学学报（自然科学版）, 2010, 28(3): 20-23.

JIA Bao-hua. A Strictly Stationary Associated Random Sequence Which Unsatisfythe Central Limit Theorem[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 20-23.

参考文献

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