Abstract

In this article, complete and complete integral convergence theorems are obtained for arrays of row wise widely negative dependent random variables under the sub-linear expectations. We improve the results by (Lin and Feng 2019 Lin, Y. W., and X. W. Feng. 2019. Complete convergence and strong law of large numbers for arrays of random variables under sublinear expectations. Communications in Statistics: Theory and Methods. Advance online publication. doi:https://doi.org/10.1080/03610926.2019.1625924. [Google Scholar]) and extend some complete moment convergence theorems in (Wu, Wang, and Rosalsky 2018 Wu, Y., X. J. Wang, and A. Rosalsky. 2018. Complete moment convergence for arrays of rowwise widely orthant dependent random variables. Acta Mathematica Sinica, English Series 34 (10):1531–48. doi:https://doi.org/10.1007/s10114-018-7173-z.[Crossref], [Web of Science ®] , [Google Scholar]) from the classical probability space to the sub-linear expectation space.

摘要

在本文中，得到了在次线性期望下，对逐行宽负相关随机变量数组的完全和完全积分收敛定理。我们通过 (Lin and Feng 2019 林、YW和XW冯。2019 年。亚线性期望下随机变量数组的完全收敛和强大数定律。统计通讯：理论和方法。提前在线发布。doi：https://doi.org/10.1080/03610926.2019.1625924。 [Google Scholar] ) 并在 (Wu, Wang, and Rosalsky2018 Wu, Y.、XJ Wang和A. Rosalsky。2018 年。行宽正交相关随机​​变量数组的完全矩收敛。数学学报，英文系列34 (10): 1531 – 48。doi：https://doi.org/10.1007/s10114-018-7173-z。[Crossref], [Web of Science ®]  , [Google Scholar] ) 从经典概率空间到次线性期望空间。