Complete Convergence of Weighted Sums for Arrays of Rowwise m-negatively Asso ciated Random Variables

In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions.     

行为混合阵列加权和的收敛性

本文研究了行为混合阵列加权和的收敛性.利用混合序列的Rosenthal型最大值不等式,讨论了混合阵列加权和的L1收敛性,依概率收敛性,几乎处处收敛性,及完全收敛性之间的等价关系,推广了行独立随机变量阵列相应的结果.     

行为NA的随机变量阵列加权和的完全收敛性(Ⅱ)

本文研究了行为NA的随机变量阵列加权和的完全收敛性,推广了行独立随机变量阵列相应的结果.且得到了任意随机变量阵列加权和完全收敛的一个定理.     

Complete Convergence for Weighted Sums of Arrays of Rowwise Asymptotically Almost Negative Associated Random Variables

Let be an array of rowwise asymptotically almost negative associated (AANA, in short) random variables. The complete convergence for weighted sums of arrays of rowwise AANA random variables is established under some general moment conditions. The result obtained in the paper generalizes and improves the corresponding one for negatively associated random variables.     

行为负相依随机变量阵列加权和的完全收敛性

本文研究了行为NOD随机变量阵列加权和的完全收敛性.运用NOD随机变量列的矩不等式以及截尾的方法,得到了关于行为NOD随机变量阵列加权和的完全收敛性的充分条件.利用获得的充分条件,推广了Baek(2008)关于行为NA随机变量阵列加权和的完全收敛性的结论,得到了比吴群英(2012)更为一般的结果.     

行为NA的随机变量阵列加权和的完全收敛性

In this paper we obtain theorems of complete convergence for weighted sums of arrays of rowwise negatively associated （NA） random variables. These results improve and extend the corresponding results obtained by Sung （2007）, Wang et al. （1998） and Li et al. （1995） in independent sequence case.     

行为ND随机变量阵列加权和的完全收敛性

在非同分布的情况下,给出了行为ND随机变量阵列加权和的完全收敛性的充分条件,所得结果部分地推广了独立随机变量和NA随机变量的相应结果.作为其应用,获得了ND随机变量序列加权和的Marcinkiewicz-Zygmund型强大数定律.     

Complete convergence for weighted sums of LNQD random variables

In this paper, we study the complete convergence for weighted sums of linearly negative quadrant dependent (LNQD) random variables based on the exponential bounds. In addition, we present some complete convergence for arrays of rowwise LNQD random variables.     

NA随机变量阵列的完全矩收敛性

利用NA随机变量的矩不等式和截尾方法,研究了NA随机变量阵列的完全矩收敛性,给出了证明NA随机变量阵列完全矩收敛性的一些充分条件.所得结果推广了已有文献关于NA随机变量的相应结果.     

Complete convergence of weighted sums for arrays of rowwise φ-mixing random variables

In this paper, we establish the complete convergence and complete moment convergence of weighted sums for arrays of rowwise φ-mixing random variables, and the Baum-Katz-type result for arrays of rowwise φ-mixing random variables. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of φ-mixing random variables is obtained. We extend and complement the corresponding results of X. J. Wang, S. H. Hu (2012).     

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研究了负相关随机变量阵列加权和的矩完全收敛性,改进了Baek等(2008)的结果.作为应用,得到了基于负相关随机变量序列的平滑移动过程的矩完全收敛性,完善了Li等(2004)的结果.     

NA随机变量阵列加权和的矩完全收敛性

In this paper we obtain some new results on complete moment convergence for weighted sums of arrays of rowwise NA random variables.Our results improve and extend some well known results from the litera...     

On complete moment convergence of weighted sums for arrays of row-wise negatively associated random variables

Negatively associated (NA) random variables are a more general class of random variables which include a set of independent random variables and have been applied to many practical fields. In this paper, the complete moment convergence of weighted sums for arrays of row-wise NA random variables is investigated. Some sufficient conditions for complete moment convergence of weighted sums for arrays of row-wise NA random variables are established. Moreover, under the weaker conditions, we extend the results of Baek et al. [J. Korean Stat. Soc. 37 (2008), pp. 73–80] and Sung [Abstr. Appl. Anal. 2011 (2011)]. As an application, the complete moment convergence of moving average processes based on an NA random sequence is obtained, which improves the result of Li and Zhang [Stat. Probab. Lett. 70 (2004), pp. 191–197 ].     

m-NA随机阵列的完全收敛性的一个注记

本文研究了行m-NA随机阵列的完全收敛性.利用文[8]中结果获得了m-NA列最大部分和的一个概率不等式,并根据该不等式和截尾的方法,探讨了行m-NA随机阵列的完全收敛性,获得了与行NA随机阵列情形类似的结果,简化了文[5]中定理1的证明.     

行为NSD随机变量阵列加权和的q阶矩完全收敛性

利用Hoffmann-Jφrgensen型概率不等式和截尾法,获得了行为NSD随机变量阵列加权和的q阶矩完全收敛性的充分条件.利用这些充分条件,不仅推广和深化梁汉营等(2010)和郭明乐等(2014)的结论,而且使他们的证明过程得到了极大地简化.     

On Some Conditions for Complete Convergence for Arrays of Rowwise Negatively Dependent Random Variables

Abstract

This note contains some sufficient conditions for the complete convergence in the strong law of large numbers for arrays of rowwise negatively dependent random variables. Moreover, the rowwise sums are randomly indexed.     

行为NA的随机变量阵列的完全收敛性

根据 NA序列的一个矩不等式 ,研究了行为 NA的随机变量阵列的完全收敛性和依概率收敛性 ,所得结果 ,推广了行独立随机变量阵列相应的结果     

H可积下的相依随机变量和的完全收敛性质

在满足H可积的条件下,利用随机变量的截尾方法,以及相关引理,给出了行内两两NQD序列以及p混合条件的随机组列部分和的完全收敛定理以及强大数定理．     

NOD随机变量阵列加权乘积和的强极限定理

本文研究了行为NOD随机变量阵列加权乘积和的完全收敛性和强稳定性,推广和改进了文献[1]和[2]在NA情形时的结果以及[4]在独立同分布情形时的结果.     

On the Strong Rates of Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables

A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.