Some Kinds of Uniform Integrability and Laws of Large Numbers in Noncommutative Probability

被引：4

作者：

Nguyen Van Quang ^{[1
]}

Do The Son ^{[2
]}

Le Hong Son ^{[3
]}

机构：

[1] Vinh Univ, Dept Math, Vinh City, Nghe An Provinc, Vietnam

[2] Ind Univ Ho Chi Minh City, Fac Fundamental Sci, Thanh Hoa Campus, Ho Chi Minh City, Vietnam

[3] Vinh Univ Technol Educ, Fac Gen Educ, Vinh City, Vietnam

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2018年 / 31卷 / 02期

关键词：

Uniform integrability; Law of large numbers; Measurable operator; von Neumann algebra; Bilateral almost uniform convergence; CESARO ALPHA-INTEGRABILITY; WEAK LAW;

D O I：

10.1007/s10959-017-0740-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The aim of this paper is to propose some equivalent conditions of uniform integrability for a sequence of measurable operators. Based on this result, we introduce some kinds of CesA ro uniform integrability in noncommutative probability. In addition, several results on the laws of large numbers related to these notions are established. Our results not only generalize related previously reported results but also improve them.

引用

页码：1212 / 1234

页数：23

共 50 条

[21] On uniform laws of large numbers for smoothed empirical measures
Gaenssler, P
Rost, D
HIGH DIMENSIONAL PROBABILITY II, 2000, 47 : 79 - 87
[22] Laws of large numbers for ratios of uniform random variables
Adler, Andre
OPEN MATHEMATICS, 2015, 13 : 571 - 576
[23] Sequential complexities and uniform martingale laws of large numbers
Rakhlin, Alexander
Sridharan, Karthik
Tewari, Ambuj
PROBABILITY THEORY AND RELATED FIELDS, 2015, 161 (1-2) : 111 - 153
[24] On the notions of stochastic domination and uniform integrability in the Cesàro sense with applications to weak laws of large numbers for random fields*
Thai Van Dat
Nguyen Chi Dzung
Vo Thi Hong Van
Lithuanian Mathematical Journal, 2023, 63 : 44 - 57
[25] NOTE ON SOME STRONG LAWS OF LARGE NUMBERS
CHUNG, KL
AMERICAN JOURNAL OF MATHEMATICS, 1947, 69 (01) : 189 - 192
[26] On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators
Harry Van Zanten
Statistical Inference for Stochastic Processes, 2003, 6 (2) : 199 - 213
[27] Uniform laws of large numbers and stochastic Lipschitz-continuity
de Jong, RM
JOURNAL OF ECONOMETRICS, 1998, 86 (02) : 243 - 268
[28] Laws of large numbers in non-Archimedean probability theory
Khrennikov, AY
IZVESTIYA MATHEMATICS, 2000, 64 (01) : 207 - 219
[29] G-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space
Castaing, C
de Fitte, PR
JOURNAL OF THEORETICAL PROBABILITY, 2000, 13 (01) : 93 - 134
[30] SOME LAWS OF LARGE NUMBERS FOR NORMED LINEAR SPACES
TAYLOR, RL
PADGETT, WJ
SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A, 1974, 36 (OCT): : 359 - 368

← 1 2 3 4 5 →