L^p convergence and complete convergence for weighted sums of AANA random variables

ABSTRACT

Let {X_n, n ⩾ 1} be a sequence of asymptotically almost negatively associated (AANA, for short) random variables which is stochastically dominated by a random variable X, and {d_ni, 1 ⩽ i ⩽ n, n ⩾ 1} be a sequence of real function, which is defined on a compact set E. Under some suitable conditions, we investigate some convergence properties for weighted sums of AANA random variables, especially the L^p convergence and the complete convergence. As an application, the Marcinkiewicz–Zygmund-type strong law of large numbers for AANA random variables is obtained.

KEYWORDS:

• AANA sequence
• Weighted sums
• L^p convergence
• Complete convergence.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15
• 60F25

Acknowledgments

The authors are most grateful to the editor-in-chief and anonymous referees for careful reading of the manuscript and valuable suggestions, which helped in improving an earlier version of this article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11671012), the Natural Science Foundation of Anhui Province (1508085J06), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005), the Graduate Academic Innovation Research Project of Anhui University (yfc100025), and the Students Innovative Training Project of Anhui University (201710357185).