Weak laws of large numbers for arrays of dependent random variables

Abstract

In this paper, we establish some weak laws of large numbers for arrays of dependent random variables satisfying the conditions of a kind of uniform integrability. Our results extend and improve the corresponding ones.

Keywords::

• uniform integrability
• weak law of large numbers
• martingale difference
• pair-wise NQD sequence
• NOD sequence

2000 AMS Classification number::

• 60F05
• 60F25

Acknowledgements

The authors are most grateful to the Editor-in-Chief Saul Jacka, the Associate Editor, an editor and anonymous referees for careful reading of the manuscript and valuable suggestions which helped in improving significantly an earlier version of this paper.

Additional information

Funding

This work was supported by the NNSF of China [grant number 11171001], [grant number 11201001]; Natural Science Foundation of Anhui Province [grant number 1208085QA03], [grant number 1308085QA03].