END随机变量序列Sung型加权和的矩完全收敛性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1103-1111.

END随机变量序列Sung型加权和的矩完全收敛性

邱德华¹(),肖娟²()

¹ 广东财经大学统计与数学学院广州 510320
² 衡阳师范学院数学与统计学院湖南衡阳 421002

收稿日期:2017-05-08 出版日期:2018-12-26 发布日期:2018-12-27
作者简介:邱德华, E-mail:qiudhua@sina.com|肖娟, E-mail:xiaojhengyang@163.com
基金资助:
国家自然科学基金(11271161)

Complete Moment Convergence for Sung's Type Weighted Sums Under END Setup

Dehua Qiu¹(),Juan Xiao²()

¹ School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320
² School of Mathematics and Statistics, Hengyang Normal University, Hunan Hengyang 421002

Received:2017-05-08 Online:2018-12-26 Published:2018-12-27
Supported by:
Supported by the NSFC(11271161)

摘要/Abstract

摘要：

该文利用END随机变量序列部分和的Menshov-Rademacher型不等式，得到了同分布END随机变量序列的Sung型加权和的矩完全收敛性定理，推广和改进了已知的相应的一些结果.

关键词: END随机变量, 矩完全收敛, 加权和

Abstract:

In this paper, the authors study a complete moment convergence result for Sung's type weighted sums of identically distributed END random variables by utilizing the Menshov-Rademacher's inequality of the partial sums of END random variables. The result extends and improves the corresponding theorems in series of previous papers.

Key words: END random variables, Complete moment convergence, Weighted sum

中图分类号:

O211.4

邱德华, 肖娟. END随机变量序列Sung型加权和的矩完全收敛性[J]. 数学物理学报, 2018, 38(6): 1103-1111.

Dehua Qiu, Juan Xiao. Complete Moment Convergence for Sung's Type Weighted Sums Under END Setup[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1103-1111.

参考文献

1	Chow Y S . On the rate of moment complete convergence of sample sums and extremes. Bull Inst Math Acta Sinica, 1988, 16: 177- 201
2	Wu Y , Wang X J , Hu S H . Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model. Statist Probab Lett, 2017, 127: 56- 66
3	Chen P , Bai P , Sung S H . The von Bahr-Esseen moment inequality for pairwise independent random variables and applications. J Math Anal Appl, 2014, 419: 1290- 1302
4	Chen P Y , Wang D C . Complete moment convergence for sequence of identically distributed φ-mixing random variables. Acta Mathematica Sinica, 2010, 26 (4): 679- 690
5	Liang H Y , Li D L , Rosalsky A . Complete moment and integral convergence for sums of negatively associated random variables. Acta Mathematica Sinica, 2010, 26 (3): 419- 432
6	Qiu D H , Liu X D , Chen P Y . Complete moment convergence for maximal partial sums under NOD setup. J Inequal Appl, 2015, 2015: 58
7	王定成, 苏淳. B值独立同分布随机变元序列的矩完全收敛性. 应用数学学报, 2004, 27 (3): 440- 448
7	Wang D C , Su C . Moment complete convergence for sequences of B-valued iid random elements. Acta Math Appl Sin, 2004, 27 (3): 440- 448
8	邱德华, 陈平炎. END随机变量序列产生的移动平均过程的收敛性. 数学物理学报, 2015, 35A (4): 756- 768
8	Qiu D H , Chen P Y . Convergence for moving average processes under END set-up. Acta Math Sci, 2015, 35A (4): 756- 768
9	邱德华, 段振华. $\tilde \rho $混合随机变量序列加权和的矩完全收敛性. 数学物理学报, 2017, 37A (2): 265- 277
9	Qiu D H , Duan Z H . Complete moment convergence for weighted sums of $\tilde \rho $-mixing random variable sequences. Acta Math Sci, 2017, 37A (2): 265- 277
10	Sung S H . Complete convergence for weighted sums of ρ^-mixing random variables. Discrete Dyn Nat Soc, 2010, Article ID*: 630608
11	Li W , Chen P , Sung S H . Remark on convergence rate for weighted sums of ρ^-mixing random variables. Revista Real Acad Cien Exactas Fisi Natur Math, 2017, 111*: 507- 513
12	Zhang G H . Complete convergence for Sung's type weighted sums of END random variables. J Inequal Appl, 2014, 2014: 353
13	Liu L . Precise large deviations for dependent random variables with heavy tails. Statist Probab Lett, 2009, 79 (9): 1290- 1298
14	Joag-Dev K , Proschan F . Negative association of random variables with applications. Ann Statist, 1983, 11 (1): 286- 295
15	Qiu D H , Chen P Y , Antonini R G , et al. On the complete convergence for arrays of rowwise extended negatively dependent random variables. J Korean Math Soc, 2013, 50 (2): 379- 392
16	Wang X J , Hu S H , Hu T C . Complete convergence for weighted sums and arrays of rowwise END sequences. Comm Statist Theory Methods, 2013, 42: 2391- 2401
17	Wu Y F , Guan M . Convergence properties of the partial sums for sequences of END random variables. J Korean Math Soc, 2012, 49: 1097- 1110
18	Liu L . Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails. Sci China Math, 2010, 53 (6): 1421- 1434
19	Shen A T . Probability inequalities for END sequence and their applications. J Inequal Appl, 2011, 2011: 98

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