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??In this paper, by applying the moment inequality for asymptotically almost negatively associated (AANA, in short) random sequence and truncated method, the equivalent conditions of complete moment convergence of the maximum partial for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of{15},{16} and {17}, respectively.     

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.     

The Convergence of a Moving Average Process of AANA Random Variables

Based on the asymptotically almost negatively associated(AANA) random vari-ables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1+Y )] < ∞. As an application, Marcinkiewicz-Zygmund-type strong law of large numbers for this moving average process is presented in this paper.     

Equivalent Conditions of Complete qth Moment Convergence for Weighted Sums of Sequences of Negatively Orthant Dependent Random Variables

In this paper, the complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables are established. These results not only extend the corresponding results obtained by Li and Sp\v{a}taru\ucite{4}, Liang et al.\ucite{5}, Guo\ucite{6} and Gut\ucite{21} to sequences of negatively orthant dependent random variables, but also improve them.     

Strong convergence for sequences of asymptotically almost negatively associated random variables

In this article, the complete convergence for sequences of asymptotically almost negatively associated (AANA) random variables is studied. As applications, the Baum–Katz-type theorem, Hsu–Robbins-type theorem and Marcinkiewicz–Zygmund strong law of large numbers for sequences of AANA random variables are obtained.     

随机变量序列乘积和的矩完全收敛性

利用王岳宝等将乘积和转化为部分和的乘积之和的方法,研究了随机变量序列乘积和的矩完全收敛性,获得了乘积和矩完全收敛的充分条件.     

Complete moment convergence for arrays of rowwise NSD random variables

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.     

PA随机变量产生的移动平均过程的矩完全收敛性

设{ε_i:-∞i∞}是同分布正相协随机变量序列,{a_i:-∞i+∞}是绝对可和的常数列.在一定的条件下得到了移动平均过程(?)的矩完全收敛的精确渐近性.把有关负相协条件下的结果推广到正相协情形.     

Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables

In this paper, complete moment convergence for widely orthant dependent random variables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.     

同分布ρ混合序列的矩完全收敛性

获得了同分布ρ混合序列的矩完全收敛性成立的充分必要性条件,推广和改进了已有的结果.     

加权AANA随机变量和的一致强收敛速度

为了完善 AANA 序列的极限理论,利用三级数定理、Borel-Cantelli 引理及一些概率不等式,研究了AANA 随机变量序列的函数加权和。在一定的条件下,得到了其一致强收敛速度为n？13 log n,推广了关于NA随机变量序列的相应结果。     

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 ].     

B值随机元阵列的矩完全收敛性

在随机元阵列随机有界于某非负随机变量的条件下,得到了B值行独立的随机元阵列的矩完全收敛性的一些充分条件.同时研究了p型Banach空间中行独立的随机元阵列的矩完全收敛性.     

Complete moment convergence of pairwise NQD random variables

It is known that the dependence structure of pairwise negative quadrant dependent (NQD) random variables is weaker than those of negatively associated random variables and negatively orthant dependent random variables. In this article, we investigate the moving average process which is based on the pairwise NQD random variables. The complete moment convergence and the integrability of the supremum are presented for this moving average process. The results imply complete convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers for pairwise NQD sequences.     

行为ρ混合随机变量阵列的完全矩收敛性

本文假设 X ni ;i ≥1,n ≥{}1是一列行为？ρ混合随机变量阵列。在没有同分布和随机控制的假设条件下,作者讨论了？ρ混合随机变量的完全矩收敛性,所获得结果推广和改进了 Hu and Taylor （1997）,Zhu （2006）和 Wu and Zhu （2010）的相应定理。     

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 moment and integral convergence for sums of negatively associated random variables

For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE（max1≤k≤n｜Sk｜^1/q-∈bn^1/qp）^＋〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 （log n） ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.     

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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.     

B值随机元阵列矩完全收敛性的进一步讨论

完全收敛性是概率极限理论中的一个重要的概念.考虑了矩完全收敛性,在随机元阵列随机有界于某非负随机变量的条件下,通过引入函数类S,得到了B值行独立对称的随机元阵列矩完全收敛性的一些充分条件.同时得到了p型Banach空间中独立零均值随机元序列矩完全收敛性的一个充分条件.     

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