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.     

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.     

离散型随机变量密度函数的定义与探讨

使用“δ函数”定义离散型随机变量的密度函数，寻求离散型随机变量与连续型随机变量的统一处理方法．基于离散型随机变量密度函数的定义．其一维随机变量函数的密度函数以及多维随机变量的边缘密度等，均可直接利用连续型随机变量的相关结论．     

齐性球对称分布的特征

设随机变量ｘ＝（ｘ１，…，ｘｎ）＇服从球对称分布，密度函数是ｃｎ［ｆ（ｘ＇ｘ）］＾ｇ（ｎ）。最后，将其中部分结果推广到多元球对称分布的情形。     

两个n维随机变量函数的概率密度的求法

从二维随机变量函数的概率密度的求法出发,引入了n维随机变量函数的概率密度的求法,并介绍了两个常见的n维随机变量函数的概率密度的求法.     

二维随机变量条件分布函数教学的思考

本文利用条件概率的定义,由随机变量分布函数的性质,给出一般情形下随机变量条件分布函数的定义,以帮助学生更好地理解随机变量的条件分布函数的概念.     

既非离散又非连续的随机变量

讨论既非离散又非连续的随机变量,总结这类随机变量分布函数的特点,由此可进行这类随机变量类型的判定.通过举例给出既非离散又非连续型随机变量数学期望的求法.     

随机误差的分布机理

研究随机变量误差的分布函数,通过数理变形、推导证明此随机变量精确服从正态分布.     

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.     

数据非随机缺失时单变量的分布函数估计

本文研究数据非随机缺失下的分布函数估计问题.在确定缺失数据是否属于某些指定区间的前提下,对一维随机变量y的分布函数F(y)作出了估计.此时,假定数据缺失机制形式已知,但包含某未知多维参数θ.本文证明了未知参数θ的估计量(θ)的相合性和渐近正态性,也证明了分布函数F(y)的估计量F(y)的相合性和渐近正态性.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Birational aspects of the geometry of Varieties of Sums of Powers

Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.