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.     

混合序列部分和的若干收敛性质

本文研究了混合序列部分和的若干收敛性质.利用Serfling不等式推广情形,证明了一类随机变量序列部分和的一个收敛性结果,获得了混合序列部分和的收敛性,并进一步得到了混合序列加权和的强收敛性和完全收敛性,推广并改进了文[2]中有关结果.     

■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.     

混合序列加权和的完全收敛性和强收敛性

讨论了 ρ混合序列加权和的完全收敛性和强收敛性 ,推广了Stout和Thrum定理     

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。     

SOME CONVERGENCE PROPERTIES FOR THE PARTIAL SUMS OF (ρ～) MIXING SEQUENCES

本文研究了(ρ～)混合序列部分和的若干收敛性质.利用Serfling不等式推广情形,证明了一类随机变量序列部分和的一个收敛性结果,获得了(ρ～)混合序列部分和的收敛性,并进一步得到了(ρ～)混合序列加权和的强收敛性和完全收敛性,推广并改进了文[2]中有关结果.     

(ρ)混合阵列行和的若干极限定理

研究(ρ)混合阵列行和的弱收敛性、Lp收敛性和完全收敛性,目的是把独立阵列行和的相关极限定理推广到(ρ)混合阵列行和的情形,在{Xnk;1≤k≤kn↑∞,n∈N}是Cesàro一致可积的相关条件下,利用截尾、概率不等式等手法,分别获得(ρ)混合阵列行和的弱收敛性、Lp收敛性和完全收敛性定理,推广了前人的一系列结果.     

Lacunary equi-statistical convergence of positive linear operators

In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.      

Complete moment convergence for arrays of rowwise NSD random variables

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.     

广义函数Denjoy积分的收敛性问题

本文讨论广义函数De njoy积分的收敛性问题.首先给出了广义Denjoy可积函数空间中强收敛、弱收敛、弱~*收敛和广义函数Denjoy积分收敛的关系;证明拟一致收敛是广义函数Denjoy积分收敛的一个充分必要条件;最后指出了Denjoy可积广义函数列弱~*收敛与强收敛等价当且仅当原函数等度连续.     

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。     

HOMOCENTRIC CONVERGENCE BALL OF THE SECANT METHOD

A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper.For every convergence theorem,a convergence ball is respectively introduced,where the hypothesis conditions of the corresponding theorem can be satisfied.Since all of these convergence balls have the same center x~*,they can be viewed as a homocentric ball. Convergence theorems are sorted by the different sizes of various radii of this homocentric ball, and the sorted sequence represents the degree of weakness on the conditions of convergence theorems.     

Convergence of classes of subpramarts and games which become better with time

In this paper local convergence theorems for subpramarts and GBTs (games which become better with time) are presented. These results are also new for Martingales. Global convergence theorems for subpramarts and GBTs are also proved. These theorems are related to the theory of optimal stopping.     

关于拟概率测度的收敛理论

本文研究了拟概率空间上收敛概念之间的关系这一问题.利用类比的方法,在拟概率空间上提出了一些新的关于拟-随机变量的收敛概念并讨论了这些收敛概念之间的关系,获得了模糊测度下的收敛理论,推广了关于经典测度的收敛概念.     

伪Newton—B族的导出及其性质

本文对无约束优化问题提出了一类新的近似牛顿法（伪牛顿-B族）,此方法同样具有二次终止性,产生的矩阵序列保持正定对称传递性。并证明了算法的全局收敛性和超级性收敛性。     

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.     

一类位置不变的Pickands型估计量

当极值指标大于0时, 本文提出了一种位置不变的Pickands型估计量,证明了该估计量的强弱相合性, 给出了其渐近展式和强收敛速度,并对$k_2$的最优选择进行了讨论,最后利用自适应性方法对该估计量和其它Pickands型估计量进行随机模拟分析,比较该估计量的优越性.