Complete moment convergence for i.i.d. random variables

Complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

“…Remark 3.3. Theorems 3.1-3.2 extend the corresponding results obtained by Gut and Stadtmüller (2011 [8]), Qiu and Chen (2014 [17]), and Wu and Jiang (2016 [23]) from the probability space to sub-linear expectation space.…”

“…The study of complete convergence and complete moment convergence for sub-linear expectations are much more complex and difficult. The purpose of this paper is to extend corresponding results obtained by Gut and Stadtmüller (2011 [8]), Qiu and Chen (2014 [17]), and and Wu and Jiang (2016 [23]) from the probabilistic space to sub-linear expectation space. Our results are as follows.…”

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.…”

Equivalent conditions of complete moment convergence for extended negatively dependent random variables

“…Thus, complete moment convergence is one of the most important problems in probability theory. Recent results can be found in Chen and Wang (2008 [ 18 ]), Gut and Stadtmller (2011 [ 19 ]), Sung (2013 [ 20 ]), Wang and Hu (2014 [ 21 ]), Guo (2014 [ 22 ]), Qiu (2014 [ 23 ]), Qiu and Chen (2014 [ 24 ]), Wu and Jiang (2016 [ 25 ]) and Wu and Jiang (2016 [ 26 ]). In addition, Li and Spătaru (2005 [ 2 ]) obtained the following complete moment convergence theorem: Let be a sequence of independent and identically distributed (i.i.d.)…”