Weak convergence of hilbert valued martingale measures

In this paper, we discuss the property of Hilbert valued martingale measure and introduce the concept of convergence of martingale measures in distribution. The sufficient. and necessary conditions are provided for strongly orthogonal martingale measures with independent increments (Theorem 2.2). The conditions are given for convergence of martingale measures     

不同分布NA序列加权和的完全收敛性

本文讨论了不同分布NA随机变量序列加权和的完全收敛性，获得了较[7]中的定理1及定理A更为一般的安全收敛性，并得到了完全收敛速度与矩条件之间的等价关系。     

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 ].     

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.     

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.     

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.     

On the rate of convergence in the strong law of large numbers for martingales

The aim of this note is to establish the Baum–Katz type rate of convergence in the Marcinkiewicz–Zygmund strong law of large numbers for martingales, which improves the recent works of Stoica [Series of moderate deviation probabilities for martingales, J. Math. Anal. Appl. 336 (2005), pp. 759–763; Baum–Katz–Nagaev type results for martingales, J. Math. Anal. Appl. 336 (2007), pp. 1489–1492; A note on the rate of convergence in the strong law of large numbers for martingales, J. Math. Anal. Appl. 381 (2011), pp. 910–913]. Furthermore, we also study some relevant limit behaviours for the uniform mixing process. Under some uniform mixing conditions, the sufficient and necessary condition of the convergence of the martingale series is established.     

误差为鞅差序列的非参数回归模型的完全相合性

在误差为鞅差序列的条件下,利用截尾方法及鞅差序列的指数不等式,研究了非参数回归模型P-C估计量的完全收敛性,且得到了完全收敛的收敛速度.     

The convergence of moments in the martingale central limit theorem

Summary An early extension of the Lindeberg-Feller Theorem was Bernstein's discovery of necessary and sufficient conditions for the convergence of moments in the central limit theorem for sums of independent random variables. In this paper we show that Bernstein's work has a generalisation to martingales. We extend his work in both the independence and the martingale cases by showing that there exists a duality between the behaviour of the moments of the martingale and the behaviour of the sums of squares of the martingale differences. Our proofs are quite unrelated to Bernstein's and are based on Burkholder's inequalities.     

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.     

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.     

■混合随机变量序列的强收敛定律(英文)

本文建立了■混合随机变量序列的几乎处处收敛性和完全收敛性的结果.所获结果不仅把独立随机变量经典的Khintchine-Kolmogorov收敛定理和三级数收敛定理推广至■混合随机变量情形下,并在没有增加任何附加条件下改进了相关结果.     

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.     

On some generalizations of Lorentz's almost convergence

We investigate an extension of the almost convergence of G.G. Lorentz, further weakening the notion of M-almost convergence we defined in [S. Mercourakis, G. Vassiliadis, An extension of Lorentz's almost convergence and applications in Banach spaces, Serdica Math. J. 32 (2006) 71–98] and requiring that the means of a bounded sequence restricted on a subset M of converge weakly in ℓ^∞(M). The case when M has density 1 is of special interest and in this case we derive a result in the direction of the Mean Ergodic Theorem (see Theorem 2).     

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.     

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．     

The convergence space of minimal USCO mappings

A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset of all continuous functions is also addressed.      

关于任意随机可积序列的一个强收敛定理

本文研究了可积随机适应序列强收敛定理的问题.利用构造截尾停时以及鞅差序列的方法,获得了一类任意积随机适应序列的强收敛定理,推广了若干已知的结果.     

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.     

B值随机变量序列的一类局部收敛定理

研究取值于Banach空间随机变量序列的一类局部收敛定理．作为推论,得到了一类B值鞅差序列的极限定理和经典的独立随机变量序列的极限定理,