Inequalities for acceptable noncommutative random variables

被引：0

作者：

Moslehian, Mohammad Sal ^{[1
]}

Sadeghi, Ghadir ^{[2
,3
]}

Pliev, Marat ^{[4
]}

机构：

[1] Ferdowsi Univ Mashhad, Ctr Excellence Anal Algebra Struct CEAAS, Dept Pure Math, POB 1159, Mashhad 91775, Razavi Khorasan, Iran

[2] Hakim Sabzevari Univ, Dept Math & Comp Sci, POB 397, Sabzevar, Iran

[3] Ferdowsi Univ Mashhad, Ctr Excellence Anal Algebra Struct CEAAS, Mashhad, Razavi Khorasan, Iran

[4] Russian Acad Sci, Southern Math Inst, Str Markusa 22, Vladikavkaz 362027, Russia

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2020年 / 23卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Markov inequality; noncommutative probability space; trace; acceptable random variables;

D O I：

10.1142/S0219025720500125

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of acceptable noncommutative random variables and investigate their essential properties. More precisely, we provide several efficient estimation of tail probabilities of sums of noncommutative random variables under some mild conditions. Moreover, we investigate the complete convergence of a sequence of the form 1/lambda(n) Sigma(n)(i=1) x(j) in which (x(n)) is a sequence of acceptable noncommutative random variables. Our results extend some classical inequalities as well.

引用

页数：8

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