The complete moment convergence for non-identically distributed martingale-difference random fields

Abstract

In this paper, we establish the complete moment convergence for a field of martingale difference random variables, weakly upper bounded by a random variable. The results generalize and extend the complete convergences for non-identically distributed martingale-difference random fields to the case of complete moment convergences.

Keywords:

• Complete integral convergence
• Complete moment convergence
• Martingale
• Martingale difference
• Random fields
• Weakly upper bounded

2010 AMS SUBJECT CLASSIFICATION:

• 60F15

Acknowledgments

The author is very grateful to the referee for careful reading of the paper and for the valuable suggestions which allowed to improve the paper.

Additional information

Funding

This paper was supported by Wonkwang University in 2024.