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.     

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。     

关于Chover重对数律

J.Chover(1966)对分布为特征指数为α(0<α<2)的对称稳定分布的独立同分布随机变量序列部分和建立了一个重对数律,本文将此推广到分布属于特征指数为α(0<α<2)的非退化稳定分布的正则吸引场的独立同分布随机变量序列部分和上。     

NA随机变量序列的Hájeck-Rènyi不等式

本文给出了NA随机变量序列的Hájeck-Rènyi不等式,并利用它研究了NA随机变量序列的强大数律,所得结果是独立随机变量情形时相应结果的推广.而且还得到了任意随机变量序列的Hájeck-Rènyi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.     

关于~*-mixing随机变量序列的强大数定律

利用任意随机变量序列的强大数定律讨论 * -mixing随机变量序列的强大数定律 ,得到了该序列的一个强极限定理 ,推广了经典的 * mixing随机变量序列的强大数定律 .同时讨论了 m相依序列和独立随机变量序列的强大数定律 .     

关于 U-统计量和 Von-Mises 统计量的 Esseen 不等式

<正> 设{X_n}是相互独立的随机变量序列,X_n 的分布函数为 F_n(x).(?)(x,y)是二元对称函数,不妨假设 E_(?)(X_i,X_j)=0(对一切 i=(?)j).定义 U-统计量     

基于对称随机变量构造的反例

应用相关文献中对称随机变量分布函数的充要条件,阐明连续型对称随机变量概率密度的偶函数特点,以及对称随机变量的不相关性,构造一些教学反例.     

ND序列部分和的大偏差和强收敛性

利用ND随机变量序列的矩不等式、极大值不等式以及随机变量的截尾方法,重点研究了ND随机变量序列部分和的大偏差结果和强收敛性,推广了文献中一些相依随机变量序列的若干相应结果.     

负相关随机变量序列的对数律

在本文中,首先我们得到了负相关(ND)随机变量序列的指数不等式和矩不等式,然后运用这些不等式讨论了ND序列的对数律.结果,我们将独立情形下的对数律推广到ND序列情形下依然成立.     

On probability analogs of Rosenthal’s inequality

We obtain probability combinatorial inequalities for independent random variables, strengthening the well-known Rosenthal inequality. As a corollary, we prove that the generalized Rosenthal inequality for identically distributed independent functions remains valid in the case of quasinormed symmetric spaces.     

Almost sure convergence theorem and strong stability for weighted sums of NSD random variables

In this paper, Kolmogorov-type inequality for negatively superadditive dependent (NSD) random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated (NA) sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.     

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.     

从积分几何的观点看几何不等式——纪念李国平院士吴新谋教授诞辰100周年

该文先介绍一些中国数学家在几何不等式方面的工作.作者用积分几何中著名的Poincarè公式及Blaschke公式估计一随机凸域包含另一域的包含测度, 得到了经典的等周不等式和Bonnesen -型不等式.还得到了一些诸如对称混合等周不等式、Minkowski -型和Bonnesen -型对称混合等似不等式在内的一些新的几何不等式.最后还研究了Gage -型等周不等式以及Ros -型等周不等式.     

Probability inequalities for convex sets and multidimensional concentration functions

This paper derives a sharp bound for the probability that a sum of independent symmetric random vectors lies in a symmetric convex set. In one dimension this bound is an improvement of an inequality first proved by Kolmogorov. The subject of multidimensional concentration functions is also treated.     

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.     

Conditional independence,conditional mixing and conditional association

Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional version of the strong law of large numbers for conditionally independent random variables and a conditional version of the Kolmogorov’s strong law of large numbers for conditionally independent random variables with identical conditional distributions are obtained. The notions of conditional strong mixing and conditional association for a sequence of random variables are introduced. Some covariance inequalities and a central limit theorem for such sequences are mentioned.     

Strong near-epoch dependence

We introduce a new class of dependent sequences of random variables, which is a subclass of near-epoch dependent sequences, but can also be approximated by mixing sequences. For this kind of sequences of random variables, we call them strong near-epoch dependent sequences, ap-order,p > 2, (maximum) moment inequality is established under weaker dependence sizes.