Mean Convergence and Weak Laws of Large Numbers for Multidimensional Arrays of Random Elements

被引：1

作者：

Anh, Vo Thi Van ^{[1
]}

Tu, Nguyen Ngoc ^{[1
]}

机构：

[1] HCMC Univ Technol & Educ, Dept Appl Sci, 01 Vo Ngan St, Ho Chi Minh City, Vietnam

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2023年 / 46卷 / 03期

关键词：

Mean convergence; Weak law of large numbers; Banach space-valued random element; Maximum normed partial sum; RANDOM-VARIABLES; DOUBLE SUMS; MARCINKIEWICZ;

D O I：

10.1007/s40840-023-01484-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper establishes mean convergence theorems and weak laws of large numbers for the maximum normed partial sums from a d-dimensional array of random elements taking values in a real separable Banach space, irrespective of their joint distributions. The main results extend and improve several ones in the literature. The sharpness of the results is illustrated by three examples.

引用

页数：12

共 50 条

[11] Mean Convergence Theorems and Weak Laws of Large Numbers for Arrays of Measurable Operators under Some Conditions of Uniform Integrability
Nguyen Van Quang
Do The Son
Tien-Chung Hu
Nguyen Van Huan
Lobachevskii Journal of Mathematics, 2019, 40 : 1218 - 1229
[12] On the Weak Laws of Large Numbers for Compound Random Sums of Independent Random Variables with Convergence Rates
Tran, Loc Hung
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (04) : 1967 - 1989
[13] On the Weak Laws of Large Numbers for Compound Random Sums of Independent Random Variables with Convergence Rates
Loc Hung Tran
Bulletin of the Iranian Mathematical Society, 2022, 48 : 1967 - 1989
[14] Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability
Cabrera, MO
Volodin, AI
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 305 (02) : 644 - 658
[15] On the laws of large numbers for double arrays of independent random elements in Banach spaces
Andrew Rosalsky
Le Van Thanh
Nguyen Thi Thuy
Acta Mathematica Sinica, English Series, 2014, 30 : 1353 - 1364
[16] On the Laws of Large Numbers for Double Arrays of Independent Random Elements in Banach Spaces
Andrew ROSALSKY
Le Van THANH
Nguyen Thi THUY
Acta Mathematica Sinica(English Series), 2014, 30 (08) : 1353 - 1364
[17] On the Laws of Large Numbers for Double Arrays of Independent Random Elements in Banach Spaces
Rosalsky, Andrew
Le Van Thanh
Nguyen Thi Thuy
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2014, 30 (08) : 1353 - 1364
[18] MARCINKIEWICZ STRONG LAWS OF LARGE NUMBERS AND CONVERGENCE-RATES FOR ARRAYS OF INDEPENDENT RANDOM ELEMENTS IN BANACH-SPACES
SU, KL
TAYLOR, RL
STOCHASTIC ANALYSIS AND APPLICATIONS, 1992, 10 (02) : 223 - 237
[19] Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications
Aiting Shen
Andrei Volodin
Metrika, 2017, 80 : 605 - 625
[20] CONVERGENCE-RATES ON STRONG LAWS OF LARGE NUMBERS FOR ARRAYS OF ROWWISE INDEPENDENT ELEMENTS
WANG, XC
RAO, MB
YANG, XY
STOCHASTIC ANALYSIS AND APPLICATIONS, 1993, 11 (01) : 115 - 132

← 1 2 3 4 5 →