AANA随机变量序列的完全矩收敛和积分收敛的等价条件

利用AANA随机变量的Rosenthal型矩不等式,得到了AANA随机变量序列的完全矩收敛和积分收敛的等价条件.这些结果完善了已有的结果.     

一般适随机变量阵列的弱收敛

本文讨论一般适随机变量阵列行和的稳定收敛问题,其结果一般化了 Gne-denko 和 Kormogorov 关于独立随机变量阵列弱收敛的有关定理.     

随机Bernstein多项式的依分布收敛问题

利用随机的Bernstein多项式研究随机逼近问题具有一定的意义.借助弱收敛的概念,从分布函数的角度,讨论了随机Bernstein多项式依分布收敛问题.同时,与依概率收敛结果相比较,以此说明Bernstein多项式序列依分布收敛适用的范围更广.     

截断和大数律的收敛速度

本文研究了截断和大数律的收敛速度，证明了截断和（固定）完全收敛性定理以及大数律收敛速度的几个等价条件，从而推广了独立和的结果。     

几种收敛间的关系

归纳总结可测函数列关于一致收敛、近一致收敛、几乎处处收敛、依测度收敛等情况之间在一定前提条件下的关系,反例说明条件的变化将影响结论的正误,从而使收敛及其相互关系更为清晰和透彻.     

关于随机序列加权和的收敛性的注记

通过对数组加权系数的列截尾,研究了B值随机一致有界序列加权和的收敛性,获得了相应的几乎处处收敛和完全收敛到0的结果.最后建立了B值随机适应序列加权和的矩收敛定理.     

加快迭代收敛速度的两个命题

定义了单调收敛函数和交错收敛函数,并根据其收敛特点,提出并证明了加快其收敛速度的两个命题.算例表明其效果较好.     

理想收敛的若干研究及推广

在Banach空间X中利用序列的I-收敛与I*-收敛给出理想I具可加性质(AP)的等价刻画,并进一步研究弱I-收敛、弱I*-收敛、一致弱I*-收敛之间,以及弱I-收敛与收敛之间的关系,最后基于I-λ-统计收敛给出其推广:I-A-统计收敛,并以次微分映射为工具定义一族有限可加测度,用于等价刻画I-A-统计收敛,这亦是有限可加测度的一个应用体现.     

非线性Volterra积分方程解强收敛和弱收敛的充要条件

本文研究Ｂａｎａｃｈ空间中具完全正核的非线性Ｖｏｌｔｅｒｒａ积分方程解强收敛和弱收敛的充分必要条件，这里的定理推广了众多该方向的结果，例如［５，９－１０］等．     

i.i.d情况下非参数回归模型的误差密度估计的收敛性质

本文研究了i．i．d情况下非参数回归的误差密度估计的一致收敛和均方收敛，给出了一定条件下误差密度的估计量f^n(x)的一致收敛速度和均方收敛速度。     

行为NA的随机变量阵列的完全收敛性

根据 NA序列的一个矩不等式 ,研究了行为 NA的随机变量阵列的完全收敛性和依概率收敛性 ,所得结果 ,推广了行独立随机变量阵列相应的结果     

Vague Convergence of Semimartingale Random Measures

Abstract

In this paper, we introduce and research the vague convergence of semimartingale random measures in distribution. The conditions are provided for the vague convergence of semimartingale random measures and the convergence of stochastic integrals with respect to semimartingale random measures in distribution.     

随机变量序列乘积和的矩完全收敛性

利用王岳宝等将乘积和转化为部分和的乘积之和的方法,研究了随机变量序列乘积和的矩完全收敛性,获得了乘积和矩完全收敛的充分条件.     

关于m-值随机序列广义随机选择的一个强极限定理

§ 1.　Introduction　　ConsiderasequenceofBernoullitrials ,andsupposethatateachtrialthebettorhasthefreechoiceofwhetherornottobet.Asystemconsistsinfixedrulesselectingthosetrialsonwhichtheplayeristobet.ThetheoremongamblingsystemassertsthatunderanysystemthesuccessivebetsformasequenceofBernoullitrialwithunchangedprobabilityforsuccess.TheimportanceofthisstatementwasfirstrecognizedbyvonMises,whointroducedtheimpossibili tyofasuccessfulgamblingsystemasafundamentalaxiom(cf.[1 ],[2 ],[3],[4]) .Thecon …     

On a Class of Random Variational Inequalities on Random Sets

We study a class of random variational inequalities on random sets and give measurability, existence, and uniqueness results in a Hilbert space setting. In the special case where the random and the deterministic variables are separated, we present a discretization technique based on averaging and truncation, prove a Mosco convergence result for the feasible random set, and establish norm convergence of the approximation procedure.     

Some Limit Theorems for Sequences of Pairwise NQD Random Variables

In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.     

On Positive Random Objects

The idea of defining the expectation of a random variable as its integral with respect to a probability measure is extended to certain lattice-valued random objects and basic results of integration theory are generalized. Conditional expectation is defined and its properties are developed. Lattice valued martingales are also studied and convergence of sub- and supermartingales and the Optional Sampling Theorem are proved. A martingale proof of the Strong Law of Large Numbers is given. An extension of the lattice is also studied. Studies of some applications, such as on random compact convex sets in R ⁿ and on random positive upper semicontinuous functions, are carried out, where the generalized integral is compared with the classical definition. The results are also extended to the case where the probability measure is replaced by a -finite measure.     

Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables

In this paper, complete moment convergence for widely orthant dependent random variables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.     

Lr Convergence for Arrays of Rowwise Negatively Sup eradditive Dep endent Random Variables

Let {Xnk, k≥1, n≥1} be an array of rowwise negatively superadditive depen-dent random variables and {an, n ≥ 1} be a sequence of positive real numbers such that an ↑ ∞. Under some suitable conditions, Lr convergence of a1n 1max≤j≤n ied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables. fl fl fl fl jP k=1 Xnk fl fl flfl is stud-ied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables.