次线性期望下m-END序列加权和的几乎处处收敛性

Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (5): 1073-1082.

Previous Articles Next Articles

Almost Sure Convergence of Weighted Sums for m-END Sequences under Sub-linear Expectations

TAN Xili¹, DONG He¹, SUN Peiyu², ZHANG Yong²

1. College of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China;
2. Institute of Mathematics, Jilin University, Changchun 130012, China

Received:2022-11-18 Online:2023-09-26 Published:2023-09-26

Abstract

Abstract: By using Rosenthal’s inequality, we discussed almost sure convergence of weighted sums for m-END (m-extended negatively dependent) random variable sequence. Almost sure convergence of weighted sums for END sequence in the classical probability space was extended to the almost sure convergence of weighted sums for m-END random variable sequence under the sub-linear expectations.

Key words: sub-linear expectation, m-extended negatively dependent random variable sequence, weighted sum, almost sure convergence

CLC Number:

TAN Xili, DONG He, SUN Peiyu, ZHANG Yong. Almost Sure Convergence of Weighted Sums for m-END Sequences under Sub-linear Expectations[J].Journal of Jilin University Science Edition, 2023, 61(5): 1073-1082.

[1]	LIU Lunyi, WU Qunying. Almost Sure Convergence of Jamison Type Weighted Sums of END Sequence in Sub-linear Expectation Space [J]. Journal of Jilin University Science Edition, 2023, 61(4): 808-814.
[2]	HU Rong, WU Qunying. Almost Sure Convergence of Weighted Sums for END Sequences in Sub-linear Expectation Spaces [J]. Journal of Jilin University Science Edition, 2021, 59(3): 531-536.
[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]	WANG Yao, HUANG Haiwu. Convergence Properties of Weighted Sums for φMixing Random Variables Arrays [J]. Journal of Jilin University Science Edition, 2016, 54(04): 779-784.
[6]	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.
[7]	WANG Yao, HUANG Haiwu. Strong Limit Convergence Properties for Weighted Sums of φ-Mixing Sequences with Non\\|identical Distribution [J]. Journal of Jilin University Science Edition, 2015, 53(05): 939-942.
[8]	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.
[9]	LIU Dong-Mei, YANG Jin-Yang. Limit Theorem for Weighted Sums of Linear ProcessesGenerated by Mixing Sequences [J]. J4, 2012, 50(03): 421-.
[10]	LIU Jun. lmost Sure Central Limit Theorem for Weighted Sumsunder α-Weak Dependence [J]. J4, 2011, 49(01): 79-81.
[11]	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.
[12]	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.
[13]	LIU Jiding, JIANG Shihong, GUO Guangyao, LOU Liantang. Euler Strong Law of Large Numbers for Empirical Processes [J]. J4, 2007, 45(06): 899-902.
[14]	DONG Zhishan,. Marcinkiewicz’s Strong Law of Large Number for Pairwise NQD Sequences [J]. J4, 2007, 45(01): 1-4.

Almost Sure Convergence of Weighted Sums for m-END Sequences under Sub-linear Expectations

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 14

Metrics

Comments

Recommended 0