Complete convergence theorem for negatively dependent random variables under sub-linear expectations

Abstract

Under the condition that the Choquet integral exists, we study the complete convergence theorem for negatively dependent random variables under sub-linear expectation space. Two general complete convergence theorems under sub-linear expectation space are obtained, where the coefficient of weighted sum is the general function. This paper not only extends the complete convergence theorem in the traditional probability space to the sub-linear expectation space, but also extends the coefficient of weighted sum as a general function.

Keywords:

• Sub-linear expectation
• complete convergence
• negatively dependent random variables

2000 MSC:

• 60F15

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11661029, 71963008), the Support Program of the Guangxi China Science Foundation (2018GXNSFAA281011) and Innovation Project of Guangxi Graduate Education (YCSW2020175).