In this article, we study and establish complete convergence for widely negative orthant dependent random variables under the sub-linear expectations, which extend some complete convergence theorems for widely negative orthant dependent random variables from the classical probability space to sub-linear expectation space.

利用与概率空间不同的研究方法,研究次线性期望空间中独立同分布随机变量序列的加权和在某些条件下的一个强大数定律,从而将该定理从传统概率空间扩展到次线性期望空间.

In this article,we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.Our results of strong limit theorems are more general than some related results previously obtained by Thrum（1987）,Li et al.（1995） and Wu（2010） in classical probability space.

The complete convergence and complete integral convergence for randomly weighted sums when the weight is A(ni) under the sublinear expectations are established in this article. The major findings of this study are expansions of complete convergence and complete moment convergence for widely orthant-dependent (WOD) random variables in the traditional probability space.

This article aimed to investigate the almost sure convergence theorem of widely negative orthant dependent (WNOD) random variables under sub-linear expectation space. The conclusions in this essay are an extension of the corresponding conclusions in the classical probability space.

In this paper, we establish the complete convergence and complete integral convergence of partial sums for moving average process based on independent random variables under the sub-linear expectations. The results in the paper extend some convergence properties of moving average process under independent assumption from probability space to the sub-linear expectation space.

Using different research methods than probability space, this article investigates complete convergence for weighted sums of widely negative dependent random variables under sub-linear expectations. The major findings of this study are expansions of complete convergence for weighted sums of widely orthant-dependent random variables in the standard probability space.

This article aims to study and establish the Lai law for the weighted sum of extended negatively dependent random variables under sub-linear expectations. Using inequalities under sub-linear expectation spaces, we extend the complete convergence of weighted sums from classical probability space to sub-linear expectation space.

The research of convergence properties of moving average process is a challenging field of limit theorems. The aim of this article is to provide a method to prove the complete convergence and complete integral convergence of moving average process for independent random variables in sub-linear expectation space. The results obtained in the article are the extensions of some complete convergence theorems under classical probability space.

In the paper, the complete convergence and complete integral convergence for weighted sums of negatively dependent random variables under the sub-linear expectations are established. The results in the paper extend some complete moment convergence theorems from the classical probability space to the situation of sub-linear expectation space.

Limit theorems for sub-linear expectations are challenging field which have raised a large number of issues of interest recently. The aim of this article is to establish the strong limit theorems of weighted sums under a sub-linear expectation space. As applications, the strong limit theorem for extended negatively dependent and identically distributed random variables have been generalized to the sub-linear expectation space context.

In this article, we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND) random variables under the sub-linear expectations. As applications, we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations.

In this paper, convergence of series and almost sure convergence are established for weighted random variables under a sub-linear expectation space. Our results are very extensive versions which contain the related convergence of series and almost sure convergence for sequences of random variables and so on, and are extensions and improvements of classical convergence of series and almost sure convergence from the traditional probability space to the sub-linear expectation space.

假设｛Xn;n≥ 1｝是次线性期望空间(Ω,H,ê)上的独立同分布随机变量序列.本文在Cv(X2)＜∞和1imc→∞ê(X(c))=limc→∞ ê(-X(c))=0以及某类慢变化函数h(x)的条件下,将概率空间中的独立同分布随机变量加权和的一般式精确渐近性推广到次线性期望空间,获得了两个精确渐近性的一般定律,同时研究其必要性.

In this paper, some laws of large numbers are established for random variables that satisfy the Pareto distribution, so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space. Based on the Pareto distribution, we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences.

The goal of this paper is to establish complete convergence theorems for an array of row-wise END random variables under sub-linear expectation space. As applications of the exponential inequalities, we extend some complete convergence theorems from the traditional probability space to the sub-linear expectation space and our results generalize corresponding results obtained by Hu.

Let $ \{X_n; n\geq1\} $ be a sequence of independent and identically distributed random variables in a sub-linear expectation space $ (\Omega, \mathcal{H}, \hat{\mathbb{E}}) $. The necessary and sufficient conditions for the convergence rate on the laws of the logarithms and the law of the iterated logarithm are obtained.

The aim of this paper is to study and establish precise asymptotics for complete integral convergence in the law of the logarithm under the sub-linear expectation space. The methods and tools in this paper are different from those used to study precise asymptotics theorems in probability space. We extend precise asymptotics for complete integral convergence from the classical probability space to sub-linear expectation space. Our results generalize corresponding results obtained by Fu and Yang [13]. We further extend the limit theorems in classical probability space.

In this article, we establish some results on the complete convergence and complete integral convergence for weighted sums of widely negative dependent random variables under the sub-linear expectations, which extend some complete moment convergence theorems from the classical probability space to the situation of sub-linear expectation space.

In this work, by using Marcinkiewicz-Zygmund type moment inequality of asymptotically negatively associated (ANA, in short) sequences, the strong law of large numbers of linear processes with random coefficients generated by ANA sequences is studied. The obtained results extend the convergence of linear processes with constant coefficients to the case of random coefficients.