Strong convergence for weighted sums of END random variables under the sub-linear expectations

Abstract

In this article, we study strong limit theorems for weighted sums of extended negatively dependent (END, for short) random variables under the sub-linear expectations. We establish some general complete convergence theorems for weighted sums of END random variables under the sub-linear expectations. Our results partly generalize and improve the corresponding ones previously obtained by Cai (Metrika, 68:323-331, 2008), Huang and Wang (J. Inequal. Appl. 233, doi:10.1186/1029-242X-2012-233, 2012) and Wang et al. (RACSAM, 106:235-245, 2012) in the classical probability space to the sub-linear expectation space under weaker moment conditions.

Keywords:

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

2000 MR SUBJECT CLASSIFICATION:

• 60F15

Acknowledgments

We express our deep gratitude to the anonymous reviewers and editor for their constructive comments, which led to a much improved version of this paper.

Additional information

Funding

Fengxiang Feng’s research work is supported by the National Natural Science Foundation of China (11961015 and 12061027), Natural Science Foundation of Guangxi (2018GXNSFBA281019 and 2019GXNSFAA245031) and Supported by Foundation of Guilin University of Technology (GUTQDJJ2004044). Haiwu Huang’s research work is supported by the Scientific Research Fund of Hunan Provincial Education Department (18C0660), the National Statistical Science Research Project of China (2018LY05) and the State Scholarship Fund of China Scholarship Council(No.201908430242).