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

摘要

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 ) ] ∞ $C_{mathbb{V}}[|X|^{p}l(|X|^{1/lpha})]infty$ , further E ˆ ( | X | p l ( | X | 1 / α ) ) ≤ C V [ | X | p l ( | X | 1 / α ) ] ∞ $hat{mathbb {E}}(|X|^{p}l(|X|^{1/lpha}))leq C_{mathbb{V}}[|X|^{p}l(|X|^{1/lpha })]infty$ , 1 p 2 $1 p2$ ( 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 i