Banach空间上的随机加权和的收敛性

本文讨论了在P型和P凸Banach空间上的随机加权和un↑∑↑i=μnXni的r平均收敛性及依概率收敛性，并从给出了满足这些收敛性的充分与必要条件。在以往的文献中讨论的随机加权多为n↑∑↑i=1αniXi这种形式，而本文给出了在更一般情况下随机加权和的收敛性，并对以前的一些定理作了一些适当推广。     

B值随机元阵列加权和的Lr收敛性

设B是实可分的Banach空间,{Xni,Fni,un≤i≤vn,n≥1}是B值适应随机元阵 列,{αni,un≤i≤un,n≥1}是实数阵列,当0相似文献   

On weak and Moments Convergence of Randomly Indexed Sums

Let {X_n, n ? 1) be a sequence of independent random variables such that EX_n = a_n, E(X_n ? a_n)² = σ, n ? 1. Let {N_n, n ? 1} be a sequence of positive integer-valued random variables. Let us put In this paper we present necessary and sufficient conditions for weak and moments convergence of the sequence {(S-L_n)/s_n, n ? 1}, as n → ∞. Hermite polinomial type limit theorems are also considered. The obtained results extend the main theorem of M. Finkelstein and H. G. Tucker (1989).     

B值随机元阵列加权和的Lr收敛性

设B是实可分的Banach空间,{Xni,Fni,un≤i≤vn,n≥1}是B值适应随机元阵列,{αni,un≤i≤vn,n≥1}是实数阵列,当0＜r＜1或1≤r≤p且B是p可光滑时,研究了∑vni=un aniXni的Lr收敛性,所得的结果推广并改进了许多已知的结果.     

NOD随机变量随机加权部分和的完全收敛性

本文研究了NOD随机变量双下标随机加权部分和的完全收敛性,获得了一些完全矩收敛结果和完全收敛结果,从而获得了Marcinkiewicz-Zygmund型强大数律.我们的结果推广了目前已有的一些结论.进一步,我们给出一些数据模拟工作来展示收敛性结果.     

On Weak Convergence of Probability Measures in a Banach Space

Necessary and sufficient conditions are obtained for weak convergence of Borel probability distributions in a separable strictly normed Banach space with a continuous modulus of convexity. These conditions are given in terms of simultaneous convergence of the distribution functions of the norm and of all linear continuous functionals with respect to the sequence of distributions under consideration. Bibliography: 9 titles.     

Banach空间迭代序列的收敛性

先对相关基础知识进行了介绍说明,如拟增生类映象和压缩类映象,广义Lipschitz,两种迭代的迭代过程.然后阐述了目前已知相关结果,给出并论证了Mann迭代序列的收敛性.即在一致光滑的实Banach空间中,讨论并研究了带误差的Mann迭代逼近广义Lipschitz广义Φ-半压缩映象不动点的问题,改进和推广了现有的结果.     

Convergence Theorems for Best Approximations in a Nonreflexive Banach Space

In this paper, we study continuity properties of the mappingP: (x, A)→P_A(x) in a nonreflexive Banach space where PA is the metric projection onto A. Our results extend the existing convergence theorems on the best approximations in a reflexive Banach space to nonreflexive Banach spaces by using Wijsman convergence of sets.     

Complete Convergence for Randomly Weighted Sums of Random Variables Satisfying Some Moment Inequalities

For random variables and random weights satisfying Marcinkiewicz-Zygmund and Rosenthal type moment inequalities, we establish complete convergence results for randomly weighted sums of the random variables. Our results generalize those of(Thanh et al. SIAM J. Control Optim., 49,106–124(2011), Han and Xiang J. Ineq. Appl., 2016, 313(2016), Li et al. J. Ineq. Appl., 2017, 182(2017), and Wang et al. Statistics, 52, 503–518(2018).)     

有序Banach空间中的拟弱收敛及其应用

在有序Ｂａｎａｃｈ 空间中引入拟弱收敛,并表明拟弱收敛弱于弱收敛·　由此,在非紧性条件下,获得了非连续增算子的不动点,并将它应用于Ｈａｍｍｅｒｓｔｅｉｎ 型非线性积分方程     

A Note on the Rate of Complete Convergence for Weighted Sums of Arrays of Banach Space Valued Random Elements

A rate of complete convergence for weighted sums of arrays of rowwise independent Banach space valued random elements was obtained by Ahmed et al. [1 Ahmed , S.E. , Giuliano Antonini , R. , and Volodin , A. 2002 . On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes . Statist. Probab. Lett. 58 : 185 – 194 . [Google Scholar]]. Recently, Sung and Volodin [2 Sung , S.H. , and Volodin , A.I. 2006. On the rate of complete convergence for weighted sums of arrays of random elements. J. Korean Math. Soc. 43:815–828.[Crossref], [Web of Science ®] , [Google Scholar]], Chen et al. [3 Chen , P. , Sung , S.H. , and Volodin , A.I. 2006 . Rate of complete convergence for arrays of Banach space valued random elements . Siberian Adv. Math. 16 : 1 – 14 . [Google Scholar]], and Kim and Ko [4 Kim , T.S. , and Ko , M.H. 2008 . On the complete convergence of moving average process with Banach space valued random elements . J. Theor. Probab. 21 : 431 – 436 . [Google Scholar]] solved an open question posed by Ahmed et al. In this article, we improve and complement the result of Ahmed et al. The method used in this article is simpler than those in Ahmed et al., Sung and Volodin, Chen et al., and Kim and Ko.     

p-Frames in Separable Banach Spaces

Let X be a separable Banach space with dual X ^*. A countable family of elements {g _i }X ^* is a p-frame (1 p ) if the norm _X is equivalent to the ^p -norm of the sequence {g _i ()}. Without further assumptions, we prove that a p-frame allows every gX ^* to be represented as an unconditionally convergent series g=d _i g _i for coefficients {d _i } ^q , where 1/p+1/q=1. A p-frame {g _i } is not necessarily linear independent, so {g _i } is some kind of overcomplete basis for X ^*. We prove that a q-Riesz basis for X ^* is a p-frame for X and that the associated coefficient functionals {f _i } constitutes a p-Riesz basis allowing us to expand every fX (respectively gX ^*) as f=g _i (f)f _i (respectively g=g(f _i )g _i ). In the general case of a p-frame such expansions are only possible under extra assumptions.     

Strong Convergence of an Inexact Proximal Point Algorithm in a Banach Space

Journal of Optimization Theory and Applications - By using our own approach, we study the strong convergence of an inexact proximal point algorithm with possible unbounded errors for a maximal...     

Banach空间中3类问题公共解的弱收敛定理

在2-一致凸、一致光滑的Banach空间,引入了一个迭代序列来逼近3个集合的公共点,这3个集合分别是平衡问题的解集、变分不等式的解集和相对非扩张映射的不动点集.表明了这一序列弱收敛到这3个集合的公共点.     

Weak and Strong Convergence Theorems for Maximal Monotone Operators in a Banach Space

In this paper, we introduce an iterative sequence for finding a solution of a maximal monotone operator in a uniformly convex Banach space. Then we first prove a strong convergence theorem, using the notion of generalized projection. Assuming that the duality mapping is weakly sequentially continuous, we next prove a weak convergence theorem, which extends the previous results of Rockafellar [SIAM J. Control Optim. 14 (1976), 877–898] and Kamimura and Takahashi [J. Approx. Theory 106 (2000), 226–240]. Finally, we apply our convergence theorem to the convex minimization problem and the variational inequality problem.     

两指标B值鞅的A.S.收敛性与B空间的Radon-Nikodym性

本文证明了在F4条件下，任一Llog+L有界的两指标B值鞅几乎处处收敛到一可积的B值随机变量当且仅当B空间有Radon-Nikodym性质．进一步还证明了在更弱的局部F4条件下，上述结论也成立．     

On Almost Sure Behavior of Sums of Independent Banach Space Valued Random Variables

Levy's strong law of large numbers is extended to the Banach space and Chover type laws of the iterated logarithm are proved for random variables which do not necessarilly belong to the domain of normal attraction of a stable law. Also characterizations of Banach spaces in which conditions on the summands imply the above strong laws are given.