Complete moment convergence of moving-average process generated by a class of random variables

ABSTRACT

In this article, we establish the complete moment convergence of a moving-average process generated by a class of random variables satisfying the Rosenthal-type maximal inequality and the week mean dominating condition. On the one hand, we give the correct proof for the case p = 1 in Ko (2015); on the other hand, we also consider the case αp = 1 which was not considered in Ko (2015). The results obtained in this article generalize some corresponding ones for some dependent sequences.

KEYWORDS:

• Complete moment convergence
• Moving-average process
• Rosenthal-type maximal inequality
• Slowly varying function
• Weak mean domination.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15

Acknowledgments

The authors are most grateful to the Editor-in-Chief Prof. N. Balakrishnan and three anonymous referees for a careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this article.

Funding

This work was supported by the National Natural Science Foundation of China (11501004, 11501005, 11526033, 11671012), the Natural Science Foundation of Anhui Province (1508085J06), The Key Projects for Academic Talent of Anhui Province (gxbjZD2016005), the Quality Engineering Project of Anhui Province (2016jyxm0047), and the Students Innovative Training Project of Anhui University (201610357346).