PA序列部分和完全收敛性的进一步探讨

通过讨论矩的存在性与部分和尾概率级数收敛性的关系,给出了PA序列部分和的完全收敛性,获得了PA序列与独立序列类似的强极限性质.     

两两PQD序列的完全收敛性和强大数定律

给出两两PQD序列部分和的几个不等式,研究了一类广泛的随机变量序列两两PQD列的收敛性质,得到了与PA序列相类似的完全收敛性和强大数定律的结果.     

二阶矩限制下的Hajek-Renyi型不等式及其应用

在二阶矩限制下,获得了Hajek-Renyi型不等式,并给出了结果在PA,NA,Lr-混合序列场合下的应用.推广了Prakasa Rao关于PA序列的结果.     

二阶矩限制下的Hajek-Renyi型

在二阶矩限制下，获得了Hajek-Renyi型不等式，并给出了结果在PA，NA，L^T混合序列场合下的应用，推广了Prakasa Rao关于PA序列的结果。     

PA序列的Hájek-Rényi型不等式及强大数定律(英文)

本文给出了零均值PA序列的一个新的Hájek-Rényi型不等式,该不等式推广了文献[9]中的结果.此外,本文还得到了零均值PA序列的一个Brunk-Prokhorov型强大数定律.     

两两PQD序列的一个收敛性质

研究了一类广泛的随机变量序列两两PQD列的收敛性质,得到了与PA序列相类似的完全收敛性和强大数定律的结果.     

LPQD列的Hajek-Renyi型不等式及其应用

本文证明了LPQD随机变量序列的Hajek-Renyi型不等式,并由此分别得到一个LPQD序列加权和的可积性定理和强收敛定律,所得结果分别推广了Prakaso Rao,Birkel和Matula关于PA序列的相关结论.     

一类随机变量序列部分和的强大数定律

设{Xn,n≥1}是随机变量序列.文[4]在二阶矩限制下,获得了任意随机变量序列的Hajek-Renyi型不等式,并给出了随机变量序列的强大数定律.本文利用胡舒合等获得的强大数定律,给出了随机变量序列的一些几乎必然收敛性,并给出了结果在PA,NA和两两NQD序列场合下的应用.     

关于PA列部分和与乘积和的Marcinkiewicz型强大数律

Birkel(1989)d在方差存在的条件下，证明了不同分布PA列部分和的Kolmogorov型强大数律.本文取消了方差存在的限制，在合理的矩条件下证明了更一般的不同分布PA列部分和与乘积和的Marcinkiewicz型强大数律，从而能将独立列的相应结果作为自己的特况．     

混合序列部分和的若干收敛性质

本文研究了混合序列部分和的若干收敛性质.利用Serfling不等式推广情形,证明了一类随机变量序列部分和的一个收敛性结果,获得了混合序列部分和的收敛性,并进一步得到了混合序列加权和的强收敛性和完全收敛性,推广并改进了文[2]中有关结果.     

�����ĸ�˹���Ǹ�������е�ǿ��������

??Examining the conditions of positively or negatively associated sequences of random variables obeying the strong law of large numbers provided by Alexander, the sequences of Gaussian random variables, nonnegative and uniformly bounded sequences of random variables with general dependent structure were studied, and the sufficient conditions for they obeying the strong law of large numbers were given. At last, an example for Gaussian sequence satisfying the strong law of large numbers was given.     

A Central Limit Theorem for Random Fields of Negatively Associated Processes

A central limit theorem for negatively associated random fields is established under the fairly general conditions. We use the finite second moment condition instead of the finite (2+)th moment condition used by Roussas.⁽¹⁵⁾ A similar result is also given for positively associated sequences.     

How much are increasing sets positively correlated?

Two upward directed sets of sequences of zeroes and ones are positively correlated. We provide a lower bound on the correlation, in function of how much the two sets simultaneously depend on the same coordinates.Work partially supported by an NSF grant.     

NA样本回归函数估计的强相合性

在ＮＡ相依样本下研究非参数回归函数加权核估计的相合性,获得了一些较弱的充分条件,与此同时对ＮＡ序列给出一个简洁实用的Ｂｅｒｎｓｔｅｉｎ型不等式。     

On admissibility of the resolvent of discrete Volterra equations

Suppose that a pair of sequence spaces is admissible with respect to a discrete linear Volterra operator. This paper gives sufficient conditions for the same pair of spaces to be admissible with respect to the associated resolvent operator. The spaces considered include spaces of weighted bounded and weighted convergent sequences. Classes of discrete kernels are discussed for which the appropriate weight sequences are not purely exponential, but the product of an exponential and a slowly decaying sequence.     

A Note on the Uniform Laws for Dependent Processes Via Coupling

In this note we investigate the coupling of a class of dependent sequences with an independent one having the same marginal distributions. This method is then used to prove that a uniform law of averages for this class holds if a similar law holds for the associated independent sequence.     

A connection between supermodular ordering and positive/negative association

In this paper, we show that a vector of positively/negatively associated random variables is larger/smaller than the vector of their independent duplicates with respect to the supermodular order. In that way, we solve an open problem posed by Hu (Chinese J. Appl. Probab. Statist. 16 (2000) 133) refering to whether negative association implies negative superadditive dependence, and at the same time to an open problem stated in Müller and Stoyan (Comparison Methods for Stochastic Modes and Risks, Wiley, Chichester, 2002) whether association implies positive supermodular dependence. Therefore, some well-known results concerning sums and maximum partial sums of positively/negatively associated random variables are obtained as an immediate consequence. The aforementioned result can be exploited to give useful probability inequalities. Consequently, as an application we provide an improvement of the Kolmogorov-type inequality of Matula (Statist. Probab. Lett. 15 (1992) 209) for negatively associated random variables. Moreover, a Rosenthal-type inequality for associated random variables is presented.     

Thin sequences and the Gram matrix

We provide a new proof of Volberg’s Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 ≤ p ≤ ∞.     

On the strong convergence rate for positively associated random variables

For sequences of the positively associated random variables which are strictly weaker than the classical associated random ones introduced by Esary et al. (1967) [7], strong convergence rate is obtained, which reaches the available one for independent random variables in terms of Berstein type inequality. Further, we give the corresponding precise asymptotics with respect to the rate mentioned above, which extend and improve the relevant results in Fu (2009) [8].