scholarly journals STRONG LIMIT THEOREMS FOR WEIGHTED SUMS OF NOD SEQUENCE AND EXPONENTIAL INEQUALITIES

2011 ◽  
Vol 48 (5) ◽  
pp. 923-938 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Andrei I. Volodin
Keyword(s):  
Limit Theorems ◽  
Weighted Sums ◽  
Strong Limit ◽  
Exponential Inequalities ◽  
Nod Sequence

scholarly journals On strong limit theorems for negatively superadditive dependent random variables

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1541-1547
Author(s):  
Yongjun Zhang
Keyword(s):  
Strong Convergence ◽  
Limit Theorems ◽  
Complete Convergence ◽  
Convergence Property ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Limit ◽  
Nsd Random Variables ◽  
Independent Identically Distributed

In this paper, we obtain strong convergence property for Jamison weighted sums of negatively superadditive dependent (NSD, in short) random variables, which extends the famous Jamison theorem. In addition, some sufficient conditions for complete convergence for weighed sums of NSD random variables are presented. These results generalize the corresponding results for independent identically distributed random variables to the case of NSD random variables without assumption of identical distribution.

Some strong limit theorems for weighted sums of measurable operators

2021 ◽  
Author(s):  
Nguyen Van Huan ◽  
Nguyen Van Quang
Keyword(s):  
Uniform Convergence ◽  
Limit Theorems ◽  
Weighted Sums ◽  
Strong Limit ◽  
Strong Law ◽  
Noncommutative Version ◽  
Large Numbers ◽  
Measurable Operators ◽  
Almost Uniform Convergence ◽  
Independent Identically Distributed

The aim of this study is to provide some strong limit theorems for weighted sums of measurable operators. The almost uniform convergence and the bilateral almost uniform convergence are considered. As a result, we derive the strong law of large numbers for sequences of successively independent identically distributed measurable operators without using the noncommutative version of Kolmogorov’s inequality.

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