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 $C_{\mathbb{V}}[|X|^{p}l(|X|^{1/\alpha})]<\infty$
 , further $\hat{\mathbb {E}}(|X|^{p}l(|X|^{1/\alpha}))\leq C_{\mathbb{V}}[|X|^{p}l(|X|^{1/\alpha })]<\infty$
 , $1< p<2$
 (
 $l(x)>0$
 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.

/pdf/complete-convergence-and-complete-moment-convergence-for-4vbh9clmjf.pdf

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

In this paper, we first study convergence rates in the law of large numbers for independent and identically distributed random variables. We obtain a strong Lp-convergence version and a str...

Convergence rates in the law of large numbers and new kinds of convergence of random variables

Limit theorems of sub-linear expectations are challenging field that has attracted widespread attention in recent years. In this paper, we establish some results on complete integration convergence for weighted sums of arrays of rowwise extended negatively dependent random variables under sub-linear expectations. Our results generalize the complete moment convergence of the probability space to the sub-linear expectation space.

Complete integration convergence for arrays of rowwise extended negatively dependent random variables under the sub-linear expectations

In this paper, we research complete convergence and almost sure convergence under the sublinear expectations. As applications, we extend some complete and almost sure convergence theorems for weighted sums of negatively dependent random variables from the traditional probability space to the sublinear expectation space.

/pdf/some-types-of-convergence-for-negatively-dependent-random-fjw1huckpw.pdf

Some Types of Convergence for Negatively Dependent Random Variables under Sublinear Expectations

In this paper, we consider the complete convergence for weighted sums of negatively superadditive-dependent (NSD) random variables without assumptions of identical distribution. Some suffic...

Equivalent conditions of the complete convergence for weighted sums of NSD random variables

http://koreascience.or.kr:80/article/JAKO201717234703047.pdf

Xuejun Wang

Papers

On complete convergence and complete moment convergence for a class of random variables