Complete convergence and complete integral convergence for randomly weighted sums under the sublinear expectations

Abstract

The complete convergence and complete integral convergence for randomly weighted sums when the weight is $A_{ni}$ under the sublinear expectations are established in this article. The major findings of this study are expansions of complete convergence and complete moment convergence for widely orthant-dependent (WOD) random variables in the traditional probability space.

2020 Mathematics Subject Classification:

• 60F15

KEYWORDS:

• Sublinear expectation
• complete convergence
• complete integral convergence
• randomly weighted sums
• widely negative dependent

Acknowledgement

We are grateful to the editors and reviewers for their insightful comments on the manuscript, which will serve as a valuable guide for our thesis writing.

Additional information

Funding

This article was supported by the National Natural Science Foundation of China (12061028) and Guangxi Colleges and Universities Key Laboratory of Applied Statistics.