行为混合阵列加权和的收敛性

本文研究了行为混合阵列加权和的收敛性.利用混合序列的Rosenthal型最大值不等式,讨论了混合阵列加权和的L1收敛性,依概率收敛性,几乎处处收敛性,及完全收敛性之间的等价关系,推广了行独立随机变量阵列相应的结果.     

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.     

行为(ρ)混合阵列加权和的收敛性

本文研究了行为(ρ)混合阵列加权和的收敛性.利用(ρ)混合序列的Rosenthal型最大值不等式,讨论了(ρ)混合阵列加权和的L1收敛性,依概率收敛性,几乎处处收敛性,及完全收敛性之间的等价关系,推广了行独立随机变量阵列相应的结果.     

混合阵列的收敛性

该文引入了混合阵列的概念,讨论了混合阵列的完全收敛性与依概率收敛性.所得结果,推广了行独立随机变量阵列相应的结果.此外还得到了一般随机变量阵列的完全收敛性与依概率收敛性.     

ρ混合阵列的收敛性

该文引入了ρ～混合阵列的概念，讨论了ρ～混合阵列的完全收敛性与依概率收敛性. 所得结果，推广了行独立随机变量阵列相应的结果. 此外还得到了一般随机变量阵列的完全收敛性与依概率收敛性.     

拓扑半群上概率测度的条件组合收敛与SHIFT组合收敛

本文用部分群化的方法,研究拓扑半群上概率测度的条件组合收敛性与SHIFT组合收敛性,得到了一些充分条件,并推广了一些组合收敛性结果.     

B值独立同分布随机变元序列的矩完全收敛性

完全收敛性是概率论极限理论中一个重要的概念．本文考虑了矩完全收敛性，讨论了型-p Banach空间中独立同分布随机变元列部分和矩完全收敛性成立的充要条件，显示了矩完全收敛性和矩之间的关系，其结论与完全收敛性相比，还是有自身的特点．     

模糊格中分子网的σ-收敛性

在模糊格中引入分子网的σ－收敛性与σ－闭元等概念。研究了分子网的σ－极限点和σ－聚点的各种特征性质及其若干应用。讨论了σ－收敛性怀收敛性（θ－收敛性和Ｕｒｙｓｏｈｎ收敛性）之间的关系。     

非光滑方程组牛顿法的全局收敛性分析

通过定义一种新的*-微分,本文给出了局部Lipschitz非光滑方程组的牛顿法,并对其全局收敛性进行了研究.该牛顿法结合了非光滑方程组的局部收敛性和全局收敛性.最后,我们把这种牛顿法应用到非光滑函数的光滑复合方程组问题上,得到了较好的收敛性.     

■混合阵列行加权和最大值的若干收敛性质

讨论了■混合阵列行加权和最大值的弱收敛性、L_p收敛性和完全收敛性定理,将独立阵列的相关极限定理推广到了■混合随机阵列情形.     

Jensen's inequality for random elements in metric spaces and some applications

Jensen's inequality is extended to metric spaces endowed with a convex combination operation. Applications include a dominated convergence theorem for both random elements and random sets, a monotone convergence theorem for random sets, and other results on set-valued expectations in metric spaces and on random probability measures.     

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.     

General algorithm of random solutions for random nonlinear variational inequalities in banach Spaces *

In this paper, we study a class of random nonlinear variational inequalities in Banach spaces. By applying a random minimax inequahty obtained by Tarafdar and Yuan, some existence uniqueness theorems of random solutions for the random nonhnear variational inequalities are proved. Next, by applying the random auxiliary problem technique, we suggest an innovative iterative algorithm to compute the random approximate solutions of the random nonlinear variational inequahty. Finally, the convergence criteria is also discussed     

Asymptotic behavior of roots of random polynomial equations

We derive several new results on the asymptotic behavior of the roots of random polynomial equations, including conditions under which the distributions of the zeros of certain random polynomials tend to the uniform distribution on the circumference of a circle centered at the origin. We also derive a probabilistic analog of the Cauchy-Hadamand theorem that enables us to obtain the radius of convergence of a random power series.     

关于任意非负随机序列随机和的一类随机偏差定理

本文引入任意随机变量序列随机极限对数似然比概念,作为任意相依随机序列联合分布与其边缘乘积分布“不相似”性的一种度量,利用构造新的密度函数方法来建立几乎处处收敛的上鞅,在适当的条件下,给出了任意受控随机序列的一类随机偏差定理.     

On random variational inclusions with random fuzzy mappings and random relaxed cocoercive mappings

In this paper, we introduce and study the random variational inclusions with random fuzzy and random relaxed cocoercive mappings. We define an iterative algorithm for finding the approximate solutions of this class of variational inclusions and establish the convergence of iterative sequences generated by proposed algorithm. Our results improve and generalize many known corresponding results.     

The Law of Large Numbers and the Ito-Nisio Theorem for Vector Valued Random Fields

Strong convergence results are obtained for vector-valued random fields. Substantial development of Banach-valued random fields and summability results is needed to provide the framework for the major results since many plausible extensions fail for multi-indexed Banach-valued random variables. This development yields general convergence results for random fields in Banach spaces, including an Ito-Nisio theorem and strong laws of large numbers.     

Iterative procedures for solutions of random operator equations in Banach spaces

We construct random iterative processes for weakly contractive and asymptotically nonexpansive random operators and study necessary conditions for the convergence of these processes. It is shown that they converge to the random fixed points of these operators in the setting of Banach spaces. We also proved that an implicit random iterative process converges to the common random fixed point of a finite family of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces.     

随机加权U-过程的条件弱收敛

假定Ｆ是一个由函数组成的集合．在这篇文章中,我们研究了指标集Ｆ上２阶的随机加权Ｕ－过程的条件弱收敛性质,导出了Ｕ－过程的随机加权逼近．     

On operator-valued mixingales ∗

The objective of this work is to study certain random linear operator-valued processes. Both weak and strong operator-valued mbdngale are defined and the corresponding mbdngale convergence theorems are developed