Strong laws of large numbers for negatively dependent random variables under sublinear expectations

ABSTRACT

Recently, more and more researchers are interested in the investigation of strong laws of large numbers (SLLNs) under non additive probability. This article introduces a concept of negative dependence under sublinear expectations to investigate the SLLNs when the smallest subscript of random variables in the sample mean can change. It proves that all the cluster points of that kind of sample mean lie between an interval related to lower and upper means (or limits of sums of lower and upper means) of random variables with probability one under a lower probability.

KEYWORDS:

• Negative dependence
• Non additive probability
• Sublinear expectation
• SLLN.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15
• 28A12

Funding

This work was partially supported by the National Natural Science Foundation of China (grant No. 11501293) and the Scientific Research Foundation of Nanjing University of Science and Technology (No. AE89991) and partially supported by the National Natural Science Foundation of China (grant No. 11501292).