Complete convergence and complete integral convergence for weighted sums of widely acceptable random variables under the sub-linear expectations

Abstract

<abstract> <p>Since the concept of sub-linear expectation space was put forward, it has well supplemented the deficiency of the theoretical part of probability space. In this paper, we establish the complete convergence and complete integration convergence for weighted sums of widely acceptable (abbreviated as WA) random variables under the sub-linear expectations with the different conditions. We extend the complete moment convergence in probability space to sublinear expectation space.</p> </abstract>