Complete convergence and complete integration convergence for weighted sums of arrays of rowwise m-END under sub-linear expectations space

Abstract

In this paper, we study the complete convergence and the complete integration convergence for weighted sums of $ m $-extended negatively dependent ($ m $-END) random variables under sub-linear expectations space with the condition of $ \hat{\mathbb{E}}|X|^p\leqslant C_{\mathbb{V}}(|X|^p) < \infty $, $ p > 1/\alpha $ and $ \alpha > 3/2 $. We obtain the results that can be regarded as the extensions of complete convergence and complete moment convergence under classical probability space. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of $ m $-END random variables under the sub-linear expectations space is proved.

Keywords

• sub-linear expectations space
• rowwise m-end random variables
• complete convergence
• complete integration convergence