On the strong laws of large numbers for pairwise NQD random variables

Abstract

Let $\{X,X_n,n\ge 1\}$ be a sequence of pairwise NQD identically distributed random variables and $\{b_n,n\ge 1\}$ be a sequence of positive constants. In this article, we study the strong laws of large numbers for the sequence $\{X,X_n,n\ge 1\}$, under the general moment condition ${\sum }_{n=1}^{\infty }\mathbb{P}(\left|X\right|>b_n/\hspace{0.17em}\log \hspace{0.17em}n)<\infty$, which improve some known results.

KEYWORDS:

• Strong law of large numbers
• pairwise NQD random variables
• general moment condition
• identically distributed random variables
• Marcinkiewicz-Zygmund strong law

Additional information

Funding

This work is supported by National Natural Science Foundation of China (NSFC-11971154).