对称随机变量部分和的概率不等式

在对称随机变量分布函数关于原点的值大于或等于二分之一的基础上,阐明对称随机变量的部分和仍是对称随机变量,进一步,给出关于对称随机变量序列部分和的概率不等式.     

多维对称随机变量分布函数的充要条件

讨论了多维对称随机变量的若干性质,阐明其分量仍是对称随机变量,在此基础上,进一步给出多维对称随机变量分布函数的一个充分必要条件.     

对称随机变量序列的Hájek-Rényi型不等式和强大数律

得到了对称随机变量序列的Hájek-Rényi型不等式,并利用它研究了对称随机变量序列的强大数律.     

对称分布的矩刻画

从随机变量矩的角度给出了分布对称的充要条件,讨论了偏度、协方差与分布对称之间的关系.     

行－列可交换随机变量组列的极限定理

利用逆鞅、截尾等方法，我们得出行－列可交换随机变量组列的大数定律，作为推论，我们得到具有有限均值的行－列可交换无限组列满足强大数定律的充要条件是该组列的对角线元素不相关．再充分利用对称性及可交换性，我们得到对称可交换随机变量和的极限定理，并由此导出对称行－列可交换随机变量组列的完全收敛定理     

指数型随机三角级数的一些性质

Paley,Zygmund和Kahane等人研究过系数是Gauss随机变量序列,Steinhaus序列、Rademacher序列或更一般的独立对称随机变量的随机三角级数的a.s.收敛性、可积性、连续性.Kahane还给出了次Gauss随机三角级数a.s.表示的连续函数的连续模及轨道性质。但至今,对于系数是其它独立对称随机变量的三角级数还没有一般的结果,本文研究系数是指数型随机变量的随机三角级数的连续模、象集和水平集的性质。     

行—列可变换随机变量组列的极限定理

利用逆鞅、截尾等方法，我们得出行－列可变换随机变量组列的大数定律，作为推论，我们得到具有有限均值的行－列可变换无限组列满足强大数定律的充要条件是该组列的对角线元素不相关。再充分利用对称性及可变换性，我们得到对称可变换随机变量和的极限定理，并由此导出对称行－列可变换随机变量组列的完全收敛定理。     

委托-代理理论在保险代理激励机制中的应用

本文将委托 代理模型应用于保险人与保险代理人之间的激励机制中 ,在外生环境服从指数分布的随机变量时 ,针对对称信息与不对称信息情况分别进行讨论 .     

关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

本文研究了离散型随机变量次序统计量的分布矩阵的对称性 ,获得了二个定理 .定理 1　服从等概率二点分布或等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵 .定理 2　取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性 .     

关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

本研究了离散型随机变量次序统计量的分布矩阵的对称性,获得了二个定理。定理1服从等概率二点分布等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵。定理2取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性。     

Properties of certain symmetric stable distributions

Necessary and sufficient conditions are presented for jointly symmetric stable random vectors to be independent and for a regression involving symmetric stable random variables to be linear. The notion of n-fold dependence is introduced for symmetric stable random variables, and under this condition we determine all monomials in such random variables for which moments exist.     

Exact Estimates for Moments of Random Bilinear Forms

The present paper concentrates on the analogues of Rosenthal's inequalities for ordinary and decoupled bilinear forms in symmetric random variables. More specifically, we prove the exact moment inequalities for these objects in terms of moments of their individual components. As a corollary of these results we obtain the explicit expressions for the best constant in the analogues of Rosenthal's inequality for ordinary and decoupled bilinear forms in identically distributed symmetric random variables in the case of the fixed number of random variables.     

Asymptotic properties of random matrices and pseudomatrices

We study the asymptotics of sums of matricially free random variables, called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called ‘matricially free Gaussian operators’. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are ‘asymptotically matricially free’ whereas the corresponding symmetric random blocks are ‘asymptotically symmetrically matricially free’, where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, block-lower-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.     

Bounds on the sums of independent random variables in symmetric spaces

For a class of symmetric spaces of random variables, the equivalence of fulfilment of the upper bounds of the same type for collections of disjunctive and independent random variables is established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, February, 1991.     

Choosing joint distributions so that the variance of the sum is small

The paper considers how to choose the joint distribution of several random variables each with a given marginal distribution so that their sum has a variance as small as possible. A theorem is given that allows the solution of this and of related problems for normal random variables. Several specific applications are given. Additional results are provided for radially symmetric joint distributions of three random variables when the sum is identically zero.     

On the convergence of vector random measures

Summary The aim of this paper is to study Banach space-valued symmetric independently scattered random measures with emphasis on their convergence properties. The Vitali-Hahn-Saks Theorem, the Skorokhod theorem about the relations between the convergence a.e. and the convergence in law of random variables, and the central limit theorem for Banach valued random variables due to Hoffmann-Jorgensen, Pisier are extended to such measures.     

Limit Laws for Symmetric k-Tensors of Regularly Varying Measures

We consider the asymptotics of certain symmetric k-tensors, the vector analogue of sample moments for i.i.d. random variables. The limiting distribution is operator stable as an element of the vector space of real symmetric k-tensors.     

对称随机变量序列的收敛性

讨论了对称的随机变量序列的完全收敛性与强大数律,改进和加强了独立同分布时Baum L E,Katz M及Bai Z D,Cheng P E相应的结果.     

Operator Khintchine inequality in non-commutative probability

   Abstract. For the operator , where belongs to the Schatten class and where are non-commutative random variables with mixed moments satisfying a specific condition, we prove the following Khintchine inequality We find the optimal constants in the case when are the q-Gaussian and circular random variables. Moreover, we show that the moments of any probability symmetric measure appear as the optimal constants for some random variables. Received November 6, 1998 / in final form June 8, 2000 / Published online December 8, 2000