Complete Convergence for Weighted Sums of Widely Acceptable Random Variables under Sublinear Expectations

Using different methods than the probability space, under the condition that the Choquet integral exists, we study the complete convergence theorem for weighted sums of widely acceptable random variables under sublinear expectation space. We proved corresponding theorem which was extended to the sublinear expectations’ space from the probability space, and similar results were obtained.

Complete Convergence for END Random Variables under Sublinear Expectations

In this paper, the complete convergence theorems of partial sums and weighted sums for extended negatively dependent random variables in sublinear expectation spaces have been studied and established. Our results extend the corresponding results of classical probability spaces to the case of sublinear expectation spaces.

Several Different Types of Convergence for ND Random Variables under Sublinear Expectations

The goal of this paper is to build average convergence and almost sure convergence for ND (negatively dependent) sequences of random variables under sublinear expectation space. By using the basic definition of sublinear expectation space, Markov inequality, and C r inequality, we extend average convergence and almost sure convergence theorems for ND sequences of random variables under sublinear expectation space, and we provide a way to learn this subject.

Stein’s method for the law of large numbers under sublinear expectations

<p style='text-indent:20px;'>Peng, S. [<xref ref-type="bibr" rid="b6">6</xref>] proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein’s method. </p>

Precise Asymptotics for Complete Integral Convergence under Sublinear Expectations

The aim of this paper is to study and establish the precise asymptotics for complete integral convergence theorems under a sublinear expectation space. As applications, the precise asymptotics for p0≤p≤2 order complete integral convergence theorems have been generalized to the sublinear expectation space context. We extend some precise asymptotics for complete moment convergence theorems from the traditional probability space to the sublinear expectation space. Our results generalize corresponding results obtained by Liu and Lin (2006). There is no report on the precise asymptotics under sublinear expectation, and we provide the method to study this subject.