Strong laws of large numbers for weighted sums of extended negatively dependent random variables under sub-linear expectations

Abstract

In this paper, we study strong laws of large numbers for weighted sums of extended negatively dependent random variables under sub-linear expectation space. As an application, several results on strong laws of large numbers of ${\sum }_{i=1}^{k_n}{a}_{ni}{X}_i$ with the condition of $k_n\uparrow \infty$ and $k_n=\infty$ for the double arrays of positive real numbers $\left\{a_{ni};1\le i\le k_n,n\ge 1\right\}$ and sequences of extended negatively dependent random variables have been established in sub-linear expectations. The main results obtained in this article are the extensions of strong laws of large numbers for weighted sums of negatively dependent random variables under the traditional probability space.

Keywords:

• Sub-linear expectation
• weighted sums
• strong laws of large numbers
• extended negative dependence random variables

2000 MSC::

• 60F15

Acknowledgements

The authors are very grateful to the referees and the editors for the helpful comments and suggestions.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China (12061028), and support Program of the Guangxi China Science Foundation (2018GXNSFAA281011).