宽相依随机变量加权和的强极限定理

Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD） random variables are also obtained, which extend and improve the related known works in the literature.     

Local Limit Theorems for Sums of Power Series Distributed Random Variables and for the Number of Components in Labelled Relational Structures

A Local limit theorem for the distribution of the number of components in random labelled relational structures of size n (e.g., a type of random graphs on n vertices, random permutations of n elements, etc.) is proved as n→∞. The case when the corresponding exponential generating functions diverge at their radii of convergence is considered.     

相依随机变量列的随机和的中心极限问题

本文给出阵列框架下的相依随机变量列的随机和弱收敛和稳定收敛的充分必要条件，我们的结果与经典结果相似并囊括此方向上的所有已知结果．     

相依序列加权和的收敛性

本文在相依序列下考虑加权和的ａ．ｓ．收敛性和完全收敛性．所得结论推广并改进了［１］、［２］中有关结论．     

Limit Theorems for Non-Commutative Random Variables

We study the weak law of large numbers and the central limit theorem for non-commutative random variables. We first define the concepts of variance and expectation for probability measures on homogeneous spaces, and formulate the weak law of large numbers and the central limit theorem for probability measures on locally compact groups. Then, we consider the non-commutative case, where the homogeneous space is replaced by a C^*-algebra that is equipped with a locally compact group G of automorphisms. We define the concepts of variance and expectation in the non-commutative situation. Furthermore, we prove that the weak law of large numbers and the central limit theorem hold for non-commutative random variables on if they hold on the group G of automorphisms.     

可交换随机变量序列的随机极限定理

本文讨论了可交换随机变量序列{X_n:n≥1}的极限定理,得到了可交换随机变量序列的随机强大数律及加权和定理,并推广了文[4]中的结果.     

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设{Xni,un≤i≤vn,n≥1}与{ani,un≤i≤vn,n≥1}分别为一个随机阵列和一个常数阵列.本文首先引入了随机阵列{Xni,un≤i≤vn,n≥1}关于常数阵列{ani,un≤i≤vn,n≥1}剩余h-可积的概念,它是弱于h-可积,Cesaroα-可积等其它相关可积的定义.然后在这一可积的定义和适当的条件下,我们研究了相依随机序列加权和的强收敛性和平均收敛性,推广并改进了相关文献已有结果.     

Some Limit Theorems for Weighted Sums of Arrays of Nod Random Variables

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].     

NA随机变量加权和的收敛性

利用Rosenthal型最大值不等式,得到了NA随机变量加权和的Marcinkiewicz-Zygmund强大数定律和完全收敛性,所获结果推广和改进了一些文献中相应的结果.     

NOD随机变量加权和的极限

The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5] in independent sequence case.     

弱相依随机序列的若干新结果(英文)

设{Xn,n≥1}为-混合序列. 利用随机变量的截尾方法和-混合序列的三级数定理,讨论了-混合序列的收敛性质,并且得到了-混合序列的一类强极限定理,这些结果推广了独立序列的相应结果.最后研究了-混合序列加权和的强稳定性.     

Some Limit Results for Moving Sums of Stable Random Variables

We discuss the integral test for a moving sum of an iid symmetric stable sequence with exponent α (0 < α < 2), and the Chover-type LIL is given as a corollary. We also obtain the law of a single logarithm for moving sums of a normal sequence.     

Mixing Limit Theorems of Maximum of Absolute Sums and their Convergence Rates

Conditioned, in the sense of Rényi (Acta Math. Acad. Sci. Hungar. 9, 215–228 1958), limit theorem in the L_p-norm of the maximum of absolute sums of independent identically distributed random variables is established and its exact rate of convergence is given. The results are equivalent to establishing analogous results for the supremum of random functions of partial sums defined on C[0,1], i.e., the invariance principle. New methodologies are used to prove the results that are profoundly different from those used in Rényi (Acta Math. Acad. Sci. Hungar. 9, 215–228, 1958) and subsequent authors in proving the conditioned central limit theorem for partial sums.     

L 1-Convergence for Weighted Sums of Some Dependent Random Variables

In this article, the authors discuss the L ₁-convergence for weighted sums of some dependent random variables under the condition of h-integrability with respect to an array of weights. The dependence structure of the random variables includes pairwise lower case negative dependence and conditions on the mixing coefficient, the maximal correlation coefficient, or the ρ*-mixing coefficient. They prove that all the weighted sums have similar limiting behaviour.     

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.     

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。     

两两NQD阵列行和的若干极限定理

讨论了两两NQD阵列行和的弱收敛性、L_p收敛性和完全收敛性,在{X_(nk);1≤k≤k_n↑∞,n≥1}是Cesaro一致可积的相关条件下,获得了两两NQD阵列行和的弱收敛性、Lp收敛性和完全收敛性定理,将独立阵列行和的相关极限定理推广到了两两NQD阵列行和的情形.     

m-LNQD序列部分和的若干极限定理

作者提出了m-LNQD (m-linearly negative quadrant dependent)相依结构概念.首先给出了m-LNQD序列部分和的一个概率不等式,进而获得了m-LNQD序列的若干极限定理,推广了已有的结果.     

同分布的NA序列加权和的强大数律

讨论了同分布NA随机变量序列加权和的强大数律,所得结果推广了Z．D．Bai和P．E．Cheng及S．H．Sung的结果．     

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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.