ρ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, Vol. 37 ›› Issue (2): 265-277.

ρ混合随机变量序列加权和的矩完全收敛性

邱德华¹, 段振华²

1 广东财经大学数学与统计学院广州 510320;
2 广州铁路职业技术学院基础课部广州 510430

收稿日期:2016-05-31 修回日期:2016-11-20 出版日期:2017-04-26 发布日期:2017-04-26
作者简介:邱德华,qiudhua@sina.com;段振华,gtxyjwc@163.com
基金资助:
国家自然科学基金（11271161）

Complete Moment Convergence for Weighted Sums of ρ-Mixing Random Variable Sequences

Qiu Dehua¹, Duan Zhenghua²

1 School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320;
2 Department of Basic Courses, Guangzhou Institute of Railway Technology, Guangzhou 510430

Received:2016-05-31 Revised:2016-11-20 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the NSFC (11271161)

摘要/Abstract

摘要：

该文研究了混合随机变量序列加权和的矩完全收敛性.利用混合随机变量的Rosenthal型最大值不等式，得到了混合随机变量序列加权和的矩完全收敛性定理，这些结果推广和改进了已知的一些文献中相应结论.

关键词: ρ混合随机变量, 矩完全收敛, 加权和

Abstract:

In this paper, we discuss complete moment convergence for weighted sums of -mixing random variables. Complete moment convergence theorems for weighted sums of -mixing random variable sequences are obtained by utilizing the Rosenthal maximal type inequality, which generalize and extend the well-known results in the literature.

Key words: ρ-Mixing random variables, Complete moment convergence, Weighted sums

中图分类号:

O211.4

邱德华, 段振华. ρ混合随机变量序列加权和的矩完全收敛性[J]. 数学物理学报, 2017, 37(2): 265-277.

Qiu Dehua, Duan Zhenghua. Complete Moment Convergence for Weighted Sums of ρ-Mixing Random Variable Sequences[J]. Acta mathematica scientia,Series A, 2017, 37(2): 265-277.

参考文献

[1] Hsu P L,Robbins H.Complete convergence and the law of large numbers.Proc Natl Acad Aci USA,1947,33:25-31
[2] Li D L,Rao M B,Jiang T F,Wang X C.Complete convergence and almost sure convergence of weighted sums of random variables.J Theoret Probab,1995,8(1):49-76
[3] Liang H Y.Complete convergence for weighted sums of negatively associated random variables.Statist Probab Lett,2000,48:317-325
[4] Gut A.Complete convergence and Cesàro summation for i.i.d.random variables.Probab Theorey Relat Fields,1993,97:169-178
[5] Jing B Y,Liang H Y.Strong limit Theorems for weighted sums of negatively associated random variables.J Theoret Probab,2008,21(4):890-909
[6] Wang Y B,Liu X G,Su C.Equivalent conditions of complete convergence for independent weighted sums.Science in China(Series A),1998,41(9):939-949
[7] 邱德华.ρ随机变量加权和的收敛性.数学物理学报,2011,31A(1):132-141 Qiu D H.Convergence properties for weighted sums of ρ-mixing random variables.Acta Math Sci,2011,31A(1):132-141
[8] 邱德华.ρ随机变量阵列加权和的完全收敛性.数学学报,2014,57(1):151-162 Qiu D H.Complete convergence for weighted sums of arrays ρ-mixing random variables.Acta Math Sinica(Chin Ser),2014,57(1):151-162
[9] 邱德华,陈平炎,段振华.ρ混合随机变量序列加权和的完全收敛性.应用数学学报,2015,38(1):150-165 Qiu D H,Chen P,Duan Z H.Complete convergence for weighted sums of ρ-mixing random variables.Acta Math Appl Sin,2015,38(1):150-165
[10] Chow Y S.On the rate of moment convergence of sample sums and extremes.Bull Inst Math Acad Sin,1988,16(3):177-201
[11] 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 Wang D,Su C.Moment complete convergence for sequences of B-valued iid random elements.Acta Math Appl Sin,2004,27(3):440-448
[12] Li Y X,Zhang L X.Complete moment convergence of moving-average processes under dependence assumptions.Statist Probab Lett,2004,70(3):191-197
[13] Chen P Y.Complete moment convergence for sequences of independent random elements in Banach spaces.Stoch Anal Appl,2006,24(5):999-1010
[14] Chen P Y,Hu T C,Volodin A.Limiting behavior of moving average processes under negative association.Teor Ĭmovīr Mat Stat,2007,7:154-166
[15] Liang H Y,Li D L,Rosalsky A.Complete moment and integral convergence for sums of negatively associated random variables.Acta Math Sin(Engl Ser),2010,26(3):419-432
[16] Qiu D H,Urmeneta H,Volodin A.Complete moment convergence for weighted sums of sequences of independent random elements in Banach spaces.Collect Math,2014,65:155-167
[17] Qiu D H,Chen P Y.Complete and complete moment convergence for weighted sums of widely orthant dependent random variables.Acta Math Sin(Engl Ser),2014,30(9):1539-1548
[18] Stein C.A bound on the error in the normal approximation to the distribution of a sum of dependent random variables//Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability.Berkeley:University of California Press,1972,2:583-602
[19] Utev S,Peligrad M.Maximal inequalities and an invariance principle for a class of weakly dependent random variables.J Theoret Probab,2003,16:101-115
[20] Bryc W,Smolenski W.Moment conditions for almost sure convergence of weakly correlated random variables.Proc Amer Math Soc,1993,119:629-635
[21] Bradley R C.On the spectral density and asymptotic normality of weakly dependent random fields.J Theoret probab,1992,5:355-373
[22] Bradley R C.Equivalent mixing conditions for random fields.Ann Probab,1993,21:1921-1926
[23] 杨善朝.一类随机变量部分和的矩不等式及其应用.科学通报,1998,43(17):1823-1827 Yang S C.Some moment inequalities for partial sums of random variables and their applications.Chinese Science Bulletin,1998,43(17):1823-1827
[24] Peligrad M,Gut A.Almost sure results for a class of dependent random variables.J Theoret Probab,1999,12:87-104
[25] 吴群英.ρ混合序列的若干收敛性质.工程数数学学报,2001,18(3):58-64 Wu Q Y.Some convergence properties for ρ-mixing sequences.Journal of Engineering Mathematics,2001,18(3):58-64
[26] 吴群英.ρ混合序列加权和的完全收敛性和强收敛性.应用数学,2002,15(1):1-4 Wu Q Y.Convergence for weighted sums of ρ-mixing random sequences.Mathematica Applicata,2002,15(1):1-4
[27] Gan S X.Almost sure convergence for ρ-mixing random variable sequences.Statist Probab Lett,2004,67:289-298
[28] 邱德华,甘师信.ρ混合阵列的收敛性.数学物理学报,2005,25A(1):73-78 Qiu D H,Gan S X.Convergence of arrays of ρ-mixing random variables.Acta Math Sci,2005,25A(1):73-78
[29] 陈平炎.同分布ρ混合序列的最大值不等式及其应用研究.数学物理学报,2006,26A(5):725-730 Chen P Y.Maximal inequalities for identically distributed ρ mixing random variables and applications.Acta Math Sci,2006,26A(5):725-730