LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM FOR INDEPENDENT AND NON-IDENTICAL DISTRIBUTED RANDOM VARIABLES UNDER SUBLINEAR EXPECTATIONS

被引：0

作者：

Gao, Miaomiao ^{[1
]}

Hu, Feng ^{[1
]}

Zong, Zhaojun ^{[1
]}

机构：

[1] Qufu Normal Univ, Sch Stat, Qufu 273165, Peoples R China

来源：

DYNAMIC SYSTEMS AND APPLICATIONS | 2018年 / 27卷 / 02期

基金：

中国国家自然科学基金;

关键词：

SUB-LINEAR EXPECTATIONS; RISK; INEQUALITIES;

D O I：

10.12732/dsa.v27i2.3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study some limit theorems for random variables under sublinear expectations. First, a law of large numbers is proved for independent and non-identical distributed random variables with only finite first order moments. Second, a central limit theorem is proved for independent and non-identical distributed. random variables with only finite second order moments. These results include and extend some existing results.

引用

页码：237 / 256

页数：20

共 50 条

[31] A counterexample to the existence of a general central limit theorem for pairwise independent identically distributed random variables
Avanzi, Benjamin
Beaulieu, Guillaume Boglioni
de Micheaux, Pierre Lafaye
Ouimet, Frederic
Wong, Bernard
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 499 (01)
[32] Law of the logarithm and law of the iterated logarithm for a class of random variables with non-identical distributions
Yu, Haichao
Zhang, Yong
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2023, 52 (22) : 8169 - 8183
[33] CONVERGENCE RATES IN CENTRAL LIMIT THEOREM FOR SUMS OF A RANDOM NUMBER OF INDEPENDENT IDENTICALLY DISTRIBUTED RANDOM-VARIABLES
RYCHLIK, Z
SZYNAL, D
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1974, 22 (07): : 683 - 690
[34] Convergence rate of Peng's law of large numbers under sublinear expectations
Hu, Mingshang
Li, Xiaojuan
Li, Xinpeng
PROBABILITY UNCERTAINTY AND QUANTITATIVE RISK, 2021, 6 (03): : 261 - 266
[35] ON STRONG LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM FOR MARTINGALES
CSORGO, M
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 131 (01) : 259 - &
[36] CENTRAL LIMIT-THEOREM AND LAW OF LARGE NUMBERS IN THE MEAN
KRUGLOV, VM
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1982, 26 (04) : 813 - 815
[37] ON STRONG LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM FOR MARTINGALES
CSORGO, M
CANADIAN MATHEMATICAL BULLETIN, 1966, 9 (03): : 386 - &
[38] On the Strong Law of Large Numbers for a Sequence of Independent Random Variables
Korchevsky V.M.
Journal of Mathematical Sciences, 2017, 225 (5) : 788 - 790
[39] ON STRONG LAW OF LARGE NUMBERS FOR PAIRWISE INDEPENDENT RANDOM VARIABLES∗
Akhmiarova, A. T.
Veretennikov, A. yu.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2024, 69 (03) : 337 - 345
[40] The law of large numbers for free identically distributed random variables
Bercovici, H
Pata, V
ANNALS OF PROBABILITY, 1996, 24 (01): : 453 - 465

← 1 2 3 4 5 →