Complete integral convergence for weighted sums of negatively dependent random variables under sub-linear expectations

被引：0

作者：

Liu, Lunyi ^{[1
]}

Wu, Qunying ^{[1
]}

机构：

[1] Guilin Univ Technol, Coll Sci, Guilin 541006, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 09期

基金：

中国国家自然科学基金;

关键词：

negatively dependent; complete convergence; complete integral convergence; weighted sums; sub-linear expectation; COMPLETE MOMENT CONVERGENCE; G-BROWNIAN MOTION; STOCHASTIC CALCULUS; INEQUALITIES; THEOREM;

D O I：

10.3934/math.20231138

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, the complete convergence and complete integral convergence for weighted sums of negatively dependent random variables under the sub-linear expectations are established. The results in the paper extend some complete moment convergence theorems from the classical probability space to the situation of sub-linear expectation space.

引用

页码：22319 / 22337

页数：19

共 18 条

[1] Complete convergence and complete integral convergence of partial sums for moving average process under sub-linear expectations
Chen, Xiaocong
Wu, Qunying
[J]. AIMS MATHEMATICS, 2022, 7 (06): : 9694 - 9715
[2] Chow Y.S., 1988, B I MATH ACAD SIN, V16, P177
[3] A Complete Convergence Theorem of the Maximum of Partial Sums Under the Sub-Linear Expectations
Feng, Fengxiang
Zeng, Xiang
[J]. FILOMAT, 2022, 36 (17) : 5725 - 5735
[4] 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
[5] Complete integration convergence for arrays of rowwise extended negatively dependent random variables under the sub-linear expectations
Li, Shuyan
Wu, Qunying
[J]. AIMS MATHEMATICS, 2021, 6 (11): : 12166 - 12181
[6] 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
[7] Peng S, 2007, ABEL SYMP, V2, P541
[8] Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations
Peng ShiGe
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2009, 52 (07): : 1391 - 1411
[9] Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation
Peng, Shige
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2008, 118 (12) : 2223 - 2253
[10] Complete moment convergence for i.i.d. random variables
Qiu, Dehua
Chen, Pingyan
[J]. STATISTICS & PROBABILITY LETTERS, 2014, 91 : 76 - 82

← 1 2 →