Complete and complete integral convergence for weighted sums of arrays of rowwise widely negative dependent random variables under the sub-linear expectations

Abstract

In this article, we study complete and complete integral convergence theorems for weighted sums of arrays of rowwise widely negative dependent random variables under the sub-linear expectations. The presented results are Baum-Katz type theorems that extend the corresponding results in classical probability space to the case of sub-linear expectation space.

Keywords:

• Sub-linear expectation
• complete convergence
• complete integral convergence
• widely negative dependence

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15

Additional information

Funding

The research of the first author was supported by the National Natural Science Foundation of China (Grant No. 11571058). The authors are very grateful to the referee for the valuable comments and for pointing out some improvements of formulas in the early draft.