Complete Convergence for Weighted Sums of WOD Random Variables

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent ran-dom variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.     

NA序列部分和的矩完全收敛性

讨论了NA序列部分和的矩完全收敛性,在一定条件下获得了NA序列矩完全收敛的充要条件,显示了矩完全收敛和矩条件之间的关系,将独立同分布随机变量序列矩完全收敛的结果推广到NA序列,得到了与独立随机变量序列情形类似的结果.     

Equivalent Conditions of Complete Convergence and Complete Moment Convergence for END Random Variables

In this paper, the complete convergence and the complete moment convergence for extended negatively dependent (END, in short) random variables without identical distribution are investigated. Under some suitable conditions, the equivalence between the moment of random variables and the complete convergence is established. In addition, the equivalence between the moment of random variables and the complete moment convergence is also proved. As applications, the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established. The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.     

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.     

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.     

��ΪNA����������м�Ȩ����ȫ�����Եĵȼ�����

In this article, applying the result of complete convergence for negatively associated (NA) random variables which is obtained by Chen et al.\ucite{14}, the equivalent conditions of complete convergence for weighted sums of arrays of row-wise negatively associated random variables is investigated. As a result, the corresponding results of Liang\ucite{11} is generalized, moreover, the proof procedure is simplified greatly which is different from truncation method of Liang's. Thus, Gut's\ucite{13} result on Ces\`{a}ro summation of i.i.d. random variables is extended.     

On the convolution of Mittag–Leffler distributions and its applications to fractional point processes

We obtain the distribution of the sum of independent Mittag–Leffler (ML) random variables which are not necessarily identically distributed. Firstly we discuss the corresponding known result for independent and identically distributed ML random variables which follows as a special case of our result. Some applications of the obtained result to fractional point processes are also discussed.     

Complete Convergence for Weighted Sums of Negatively Sup eradditive Dep endent Random Variables

In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some su?cient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables.     

On a property of sums of independent variables

A result is obtained for sums of independent random variables. On the basis of the properties of a sum of random variables we obtain a conclusion with regard to the properties of the terms.     

Almost sure convergence of sums of maxima and minima of positive random variables

For a sequence of independent and identically distributed positive random variables, the almost sure convergence of sums of maxima (when suitably normalized) to appropriate constants is proved for both bounded and unbounded random variables. A similar result is also proved for sums of minima of such variables.     

Limit theorem for the maximum of dependent Gaussian random elements in a Banach space

The well-known Nisio result on the asymptotie equality for the maximum of real-valued Gaussian random variables is generalized to the case of Gaussian random variables taking values in a Banach space.     

随机变量的截尾与任意随机变量序列的强极限定理

利用随机变量的截尾研究任意随机变量序列的性质,建立了一类矩条件下任意随机变量序列的强极限定理.作为推论,得到了可列非齐次马尔可夫过程的一个强极限定理,推广了鞅差序列当1≤p≤2和p≥2时的Chow定理,相应的一些已有结果和若干经典的关于独立随机变量序列的强大数定律是本文的特例。     

Threshold Results for U-Statistics of Dependent Binary Variables

Large sample results for certain U-statistics, and related statistics, of binary dependent random variables are studied. The class of U-statistics include partial sums and polynomials of partial sums of a sequence of random variables. A very wide range of limit results are found. The form of the limit result can depend substantially on the magnitude of the appropriate normalizing sequence for the sum. Unexpectedly, the nature of the limit result also depends significantly on whether the degree of the U-statistic is even or odd. It is shown that dependence is a major factor contributing to this result. The limit results are illustrated with reference to a simple dynamic sequence of binary variables and a reinforced random walk.     

Complete and complete moment convergence for weighted sums of widely orthant dependent random variables

In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.     

Moment Complete Convergence for Weighted Sums of -Mixing Random Variables

In this paper, the authors discuss the moment complete convergence for weighted sums of -mixing random variables, and obtains the sufficient condition for moment complete convergence of -mixing sequence under some mixing rate condition, which generalize the result of moment complete convergence for weighted sums of i.i.d. random variables to -mixing random variables.     

两两NQD序列部分和的强大数定律

By using the moment inequality, maximal inequality and the truncated method of random variables, we establish the strong law of large numbers of partial sums for pairwise NQD sequences, which extends the corresponding result of pairwise NQD random variables.     

两两独立同分布序列Cesàro强大数定律的收敛速度

设{X,Xn,n≥0}是两两独立同分布的随机变量序列,11．为了证明这一结论而获得到的两两负相关随机变量序列的Cesaro强大数定律收敛速度的结果本身也是有意义的．此结果对于同分布的两两NQD序列也是对的．     

Asymptotic Property of <Emphasis Type="Italic">M</Emphasis> Estimator in Classical Linear Models Under Dependent Random Errors

In this paper, we first establish a useful result on strong convergence for weighted sums of widely orthant dependent (WOD, in short) random variables. Based on the strong convergence that we established and the Bernstein type inequality, we investigate the strong consistency of M estimators of the regression parameters in linear models based on WOD random errors under some more mild moment conditions. The results obtained in the paper improve and extend the corresponding ones for negatively orthant dependent random variables and negatively superadditive dependent random variables. Finally, the simulation study is provided to illustrate the feasibility of the theoretical result that we established.     

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.     

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 ].