Complete convergence and complete moment convergence for negatively associated sequences of random variables

Abstract

In this paper, we study the complete convergence and complete moment convergence for negatively associated sequences of random variables with EX = 0, E exp(ln α |X|) < ∞, α > 1. As a result, we extend some complete convergence and complete moment convergence theorems for independent random variables to the case of negatively associated random variables without necessarily imposing any extra conditions. Our results generalize corresponding results obtained by Gut and Stadtmüller (Stat. Probab. Lett. 81:1486-1492, 2011 and Qiu and Chen (Stat. Probab. Lett. 91:76-82, 2014). MSC: Primary 60F15

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

“…Condition (9) corresponds to the moment condition of probability space. Condition(11) is similar to condition (ii) of Theorem 2.1 of[15]. Our results extend Theorem 2.1 of[15] from the traditional probability space to sublinear expectation space.…”

“…From then on, lots of results on complete convergence for different sequences have been found under classical probability space. For instance, Wu and Jiang [11] obtained complete convergence for negatively associated sequences of random variables. Wang et al [12,13] studied complete convergence for martingale difference sequence and complete convergence for a type of random variables satisfying Rosenthal-type inequality.…”

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

“…[ 14 ], Wang et al . [ 15 ] and Wu and Jiang [ 16 ], and so on. Some recent papers had new results about complete convergence and complete moment convergence.…”

Theorems of complete convergence and complete integral convergence for END random variables under sub-linear expectations

“…Many of the related results have already been obtained in classical probability space. Now, some corresponding results were obtained by Gut and Stadtmuller [18], Qiu and Chen [19], Wu and Jiang [20] and Feng and Wang [21], we still need to perfect the complete convergence and complete integral convergence under sub-linear expectation. We establish the complete convergence and complete integral convergence for END random variables under sub-linear expectation and generalize them [22] to the sub-linear expectation space.…”