两两NQD 列的Lp 收敛性和矩完全收敛性

数学物理学报 ›› 2013, Vol. 33 ›› Issue (5): 850-859.

两两NQD 列的L_p 收敛性和矩完全收敛性

吴永锋

铜陵学院数学与计算机科学系安徽铜陵 244000

收稿日期:2011-05-30 修回日期:2012-06-12 出版日期:2013-10-25 发布日期:2013-10-25
基金资助:
教育部人文社科青年基金(12YJCZH217)、安徽高校青年人才基金(2011SQRL143)、安徽省教育厅自然科研重点项目(KJ2011A139)和安徽省自然科学基金(1308085MA03)资助.

L_p Convergence and Complete Moment Convergence for Sequences of Pairwise NQD Random Variables

WU Yong-Feng

Department of Mathematics and Computer Science, Tongling University, Anhui Tongling 244000

Received:2011-05-30 Revised:2012-06-12 Online:2013-10-25 Published:2013-10-25
Supported by:
教育部人文社科青年基金(12YJCZH217)、安徽高校青年人才基金(2011SQRL143)、安徽省教育厅自然科研重点项目(KJ2011A139)和安徽省自然科学基金(1308085MA03)资助.

摘要/Abstract

摘要：

研究了两两NQD (negatively quadrant dependend) 列的L_p 收敛性和矩完全收敛性, 获得了一些新结果, 推广和改进了已有的若干定理.

关键词: 两两NQD 列, L_p 收敛性, 矩完全收敛性

Abstract:

In this paper, the author studies L_p convergence and complete moment convergence for sequences of pairwise NQD random variables and obtains some new results, which extend the well-known theorems.

Key words: Pairwise NQD random sequences, L_p convergence, Complete moment convergence

中图分类号:

60F15

吴永锋. 两两NQD 列的L_p 收敛性和矩完全收敛性[J]. 数学物理学报, 2013, 33(5): 850-859.

WU Yong-Feng. L_p Convergence and Complete Moment Convergence for Sequences of Pairwise NQD Random Variables[J]. Acta mathematica scientia,Series A, 2013, 33(5): 850-859.

参考文献

[1] Lehmann E L. Some concepts of dependence. Ann Math Statist, 1966, 37}(5): 1137--1153

[2] Joag-Dev K, Proschan F. Negative association of random variables with applications. Ann Stat, 1983, 11(1): 286--295

[3] Newman C M. Asymptotic independence and limit theorems for positively and negatively dependent random variables//Tong Y L, ed. Inequalities in Statistics and Probability. IMS Lecture Notes Monogr Ser, 1984, 5: 127--140
(Inst Math Statist, Hayward, CA)

[4] Matula P. A note on the almost sure convergence of sums of negatively dependent random variables. Statist Probab Lett, 1992, 15(3): 209--213

[5] 吴群英. 两两NQD列的收敛性质. 数学学报, 2002, 45(3): 617--624

[6] 万成高. 两两NQD列的大数定律和完全收敛性. 应用数学学报, 2005, 28(2): 253--261

[7] Gan S X, Chen P Y. Some limit theorems for sequences of pairwise NQD random variables. Acta Math Sci (Ser B, Engl Ed), 2008, 28(2): 269--281

[8] 陈平炎. 两两NQD 随机序列的L_r收敛性. 数学物理学报, 2008, 28A(3): 447--453

[9] Li R, Yang W G. Strong convergence of pairwise NQD random sequences. J Math Anal Appl, 2008, 344(2): 741--747

[10] Gan S X, Chen P Y. Some remarks for sequences of pairwise NQD random variables. Wuhan Univ J Nat Sci, 2010, 15(6): 467--470

[11] Wu Q Y, Jiang Y Y. The strong law of large numbers for pairwise NQD random variables.J Syst Sci Complex, 2011, 24(2): 347--357

[12] Wu Y F, Guan M. Mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables. J Math Anal Appl, 2011, 377(2): 613--623

[13] Chandra T K. Uniform integrability in the Ces\`{a}ro Sence and the weak law of large numbers. Sankhya: the Indian
Yournal of Statistics (Series A), 1989, 51(3): 309--317

[14] 吴群英, 王远清, 伍艳春. NA 阵列行和最大值的若干极限定理. 应用概率统计, 2006, 22(2): 56--62

[15] Liang H Y, Su C. Complete convergence for weighted sums of NA sequences. Statist Probab Lett, 1999, 45(1): 85--95