The improvement about convergence properties for pairwise NQD random sequences

TL;DR

This paper enhances the convergence properties of pairwise NQD random sequences by improving and simplifying the generalized Kolmogorov-type three series theorem, leading to broader applicability and refined results in the field.

Contribution

The paper introduces an improved and simplified version of the generalized Kolmogorov-type three series theorem for NQD random variables, extending previous results.

Findings

Improved convergence criteria for pairwise NQD sequences.

Simplified proof of the generalized Kolmogorov-type three series theorem.

Enhanced results related to previous theorems by Wu, Shi, and Li et al.

Abstract

In this paper, the improvement about the generalized Kolmogorov-type three series theorem, in the case of NQD random variables, is obtained by different method. Furthermore, the generalized Kolmogorov-type three series theorem is simplified. From the simplified theorem, related results in Wu (Acta. Math. Sinica. 45(3), 617-624, 2002) and some main results in Shi (Acta. Math. Appl. Sin., 34(1), 122-130, 2011) and Li et al. (J. Math. Anal. Appl., 344, 741-747, 2008) are also discussed or improved in the article.