Complete convergence and complete integration convergence for weighted sums of arrays of rowwise m-END under sub-linear expectations space

被引：2

作者：

Dong, He ^{[1
]}

Tan, Xili ^{[1
]}

Zhang, Yong ^{[2
]}

机构：

[1] Beihua Univ, Coll Math & Stat, Jilin 132013, Peoples R China

[2] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 03期

关键词：

sub -linear expectations space; rowwise m -END random variables; complete convergence; complete integration convergence; DEPENDENT RANDOM-VARIABLES; G-BROWNIAN MOTION; STOCHASTIC CALCULUS; LIMIT-THEOREMS; LARGE NUMBERS; INEQUALITIES; LAWS;

D O I：

10.3934/math.2023340

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the complete convergence and the complete integration convergence for weighted sums of m-extended negatively dependent (m-END) random variables under sub-linear expectations space with the condition of E<SIC>|X|p < CV(|X|p) < infinity, p > 1/alpha and alpha > 3/2. We obtain the results that can be regarded as the extensions of complete convergence and complete moment convergence under classical probability space. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of m-END random variables under the sub-linear expectations space is proved.

引用

页码：6705 / 6724

页数：20

共 23 条

[1] Chow Y.S., 1988, B I MATH ACAD SIN, V16, P177
[2] Complete convergence and complete moment convergence for widely orthant-dependent random variables
Ding, Yang
Wu, Yi
Ma, Songlin
Tao, Xinran
Wang, Xuejun
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (16) : 8278 - 8294
[3] Complete and complete moment convergence for weighted sums of arrays of rowwise negatively dependent random variables under the sub-linear expectations
Feng, Fengxiang
Wang, Dingcheng
Wu, Qunying
Huang, Haiwu
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2021, 50 (03) : 594 - 608
[4] Moderate deviation principle for m-dependent random variables under the sub-linear expectation
Guo, Shuang
Zhang, Yong
[J]. AIMS MATHEMATICS, 2022, 7 (04): : 5943 - 5956
[5] COMPLETE CONVERGENCE AND THE LAW OF LARGE NUMBERS
HSU, PL
ROBBINS, H
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1947, 33 (02) : 25 - 31
[6] Multi-dimensional Central Limit Theorems and Laws of Large Numbers under Sub linear Expectations
Hu, Ze Chun
Zhou, Ling
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2015, 31 (02) : 305 - 318
[7] Complete convergence and complete integral convergence for weighted sums of widely acceptable random variables under the sub-linear expectations
Jia, Chengcheng
Wu, Qunying
[J]. AIMS MATHEMATICS, 2022, 7 (05): : 8430 - 8448
[8] [兰玉婷 Lan Yuting], 2018, [应用数学学报, Acta Mathematicae Applicatae Sinica], V41, P229
[9] Complete and complete integral convergence for arrays of row wise widely negative dependent random variables under the sub-linear expectations
Lu, Dawei
Meng, Yao
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2022, 51 (09) : 2994 - 3007
[10] Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables
Meng, Bing
Wang, Dingcheng
Wu, Qunying
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2022, 51 (12) : 3847 - 3863

← 1 2 3 →