Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation

Journal of Inequalities and Applications

Haoyuan Zhong¹  Qunying Wu¹ 

[1] College of Science, Guilin University of Technology;

关键词: sub-linear expectation space;    END random variables;    complete convergence;    complete moment convergence;   

DOI  :  10.1186/s13660-017-1538-1

来源: DOAJ

【 摘 要 】

Abstract In this paper, we study the complete convergence and complete moment convergence for weighted sums of extended negatively dependent (END) random variables under sub-linear expectations space with the condition of C V [ | X | p l ( | X | 1 / α ) ] < ∞ $C_{\mathbb{V}}[|X|^{p}l(|X|^{1/\alpha})]<\infty$ , further E ˆ ( | X | p l ( | X | 1 / α ) ) ≤ C V [ | X | p l ( | X | 1 / α ) ] < ∞ $\hat{\mathbb {E}}(|X|^{p}l(|X|^{1/\alpha}))\leq C_{\mathbb{V}}[|X|^{p}l(|X|^{1/\alpha })]<\infty$ , 1 < p < 2 $1< p<2$ ( l ( x ) > 0 $l(x)>0$ is a slow varying and monotone nondecreasing function). As an application, the Baum-Katz type result for weighted sums of extended negatively dependent random variables is established under sub-linear expectations space. The results obtained in the article are the extensions of the complete convergence and complete moment convergence under classical linear expectation space.

【 授权许可】

Unknown