General strong convergence for negatively associated random variables

ABSTRACT

For negatively associated (NA) random variables, we obtain two general strong laws of large numbers (SLLN) in which the coefficient of sum and the weight are both general functions. As corollaries, we obtain Marcinkiewicz-type SLLN, the logarithmic SLLN and Marcinkiewicz SLLN for NA random variables.

KEYWORDS:

• Borel-Cantelli lemma
• Negatively associated
• Strong law of large numbers
• The three series theorem.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15

Acknowledgments

We thank the referee very much for valuable suggestions and comments which improved the paper.

Additional information

Funding

Project supported by the National Natural Science Foundation of China (No. 11401548).