一类随机变量加权和的完全收敛性

Journal of Jilin University Science Edition

Previous Articles Next Articles

Complete Convergence for Weighted Sums of a Class of Random Variables

LAN Chongfeng

1. School of Economics, Fuyang Normal College, Fuyang 236037, Anhui Province, China；2. School of Economics and Management, Beijing University of Posts and Telecommunications,Beijing 100876, China; 3. Anhui Provincial Key Laboratory Regional Logistics Planning and Modern Logistics Engineering, Fuyang 236037, Anhui Province, China

Received:2015-08-17 Online:2016-05-26 Published:2016-05-20
Contact: LAN Chongfeng E-mail:lchfym@sina.com

Abstract

Abstract:

Let {X_n, n≥1} be a sequence of dependent random variables which satisfied Rosenthal type inequality. We established some new complete convergence theorems for weighted sums of a class of random variables with different distributions, and obtained the strong laws of large numbers for weighted sums of dependent random variables. Our results extend the corresponding results from the independent identically distributed case to the universal dependent random variables.

Key words: complete convergence, weighted sums, dependent random variables

CLC Number:

O212.4

LAN Chongfeng. Complete Convergence for Weighted Sums of a Class of Random Variables[J].Journal of Jilin University Science Edition, 2016, 54(03): 493-498.

[1]	HU Xueping, WANG Liuliu, YANG Rui. Convergence Properties for Maximum Weighted Sums of NSD Random Arrays [J]. Journal of Jilin University Science Edition, 2021, 59(5): 1101-1106.
[2]	LI Jie, WU Qunying. Complete Convergence and Complete Integral Convergence ofNegatively Dependent Sequences under Sublinear Expectations#br# [J]. Journal of Jilin University Science Edition, 2019, 57(2): 305-310.
[3]	LIU Yinping, HAO Guanjie. Complete Convergence for Maximum of Weighted Sumsof Rowwise (α,β) Mixing Arrays [J]. Journal of Jilin University Science Edition, 2017, 55(05): 1158-1162.
[4]	LU Dongmei, GAO Ruimei. Complete Convergence for Maximum ofWeighted Sums of Arrays of Rowwise ALNQD [J]. Journal of Jilin University Science Edition, 2016, 54(06): 1323-1327.
[5]	HU Xueping, WANG Cuiyun. Complete Convergence and Strong Convergence Propertiesfor END Random Sequences [J]. Journal of Jilin University Science Edition, 2015, 53(06): 1139-1144.
[6]	HU Zhicai, JIA Xiuli, WANG Zhenhua. Complete Convergence for Weighted Sums of Arraysof Rowwise ρ-Mixing Random Variables [J]. Journal of Jilin University Science Edition, 2014, 52(01): 51-55.
[7]	LAN Chong-Feng, TUN Qun-Yang. Complete Convergence Property for Sum of Partial Sums of I.I.D.Random Variables [J]. J4, 2012, 50(03): 507-.
[8]	LIU Dong-Mei, YANG Jin-Yang. Limit Theorem for Weighted Sums of Linear ProcessesGenerated by Mixing Sequences [J]. J4, 2012, 50(03): 421-.
[9]	XIA Baofei, WU Qunying, GUO Jin. Moment Complete Convergence for Partial Sums ofArrays 〖AKρ~D〗 Rowwise Mixing Random Variables Sequence [J]. J4, 2012, 50(01): 77-80.
[10]	HU Xueping, LI Huibao. Some Convergence Properties for Weighted Sum ofMixing Random Arrays [J]. J4, 2012, 50(01): 49-53.
[11]	LIU Jun. lmost Sure Central Limit Theorem for Weighted Sumsunder α-Weak Dependence [J]. J4, 2011, 49(01): 79-81.
[12]	FU Yan-Chi, TUN Qun-Yang. Consistency of Weighted Sums for Sequence of NA IdenticallyDistributed \|Random Variables [J]. J4, 2010, 48(1): 57-62.
[13]	ZHANG Qian, WANG Wen-Qing. Complete Convergence for Weighted Sums of Pairwise NQDRandom Arrays under Condition of h-Integrability [J]. J4, 2010, 48(02): 183-188.
[14]	LIU Xiao ping, YAN Han, WU Qunying. A Note on Complete Convergence of ρ^-Mixing Random Sequence [J]. J4, 2009, 47(02): 265-268.
[15]	LIU Ying, ZHANG Yong, DONG Zhishan，. Central Limit Theorem for Self-normalized Weighted Sumsof φ-Mixing Sequences [J]. J4, 2008, 46(04): 643-648.

Complete Convergence for Weighted Sums of a Class of Random Variables

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0