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   

B值随机元阵列的矩完全收敛性

在随机元阵列随机有界于某非负随机变量的条件下,得到了B值行独立的随机元阵列的矩完全收敛性的一些充分条件.同时研究了p型Banach空间中行独立的随机元阵列的矩完全收敛性.     

B值行独立随机元阵列的矩完全收敛性

本文研究了B值行独立的随机元阵列的矩完全收敛性.利用B值行独立的随机元阵列的概率不等式,在随机元阵列随机有界于某非负随机变量的条件下,获得了B值行独立的随机元阵列的矩完全收敛性的一些充分条件,并完善了Chow关于实值独立同分布随机变量列的矩完全收敛性的结果.     

B值随机元阵列的完全收敛性

令｛Ｘ_ｎｊ;１≤ｊ≤ｎ,ｎ≥１｝为行独立对称的Ｂ值随机元阵列     

B值随机元阵列的完全收敛性

令{X     

B值随机元阵列矩完全收敛性的进一步讨论

完全收敛性是概率极限理论中的一个重要的概念.考虑了矩完全收敛性,在随机元阵列随机有界于某非负随机变量的条件下,通过引入函数类S,得到了B值行独立对称的随机元阵列矩完全收敛性的一些充分条件.同时得到了p型Banach空间中独立零均值随机元序列矩完全收敛性的一个充分条件.     

B值随机元阵列加权和的完全收敛性

在随机元阵列随机有界的条件下,得到了行间独立B值随机元阵列加权和的完全收敛性成立的充分条件,延伸了文献[9]的主要结果和文献[6]的部分结果.     

Banach空间的型与B值随机元阵列完全收敛性的注记

该文在随机元阵列随机有界于某非负随机变量的条件下,进一步讨论了完全收敛性与Banach空间p型性质的等价性.     

B值随机元序列加权和的强收敛性

本文研究了B值随机元序列加权和的强收敛性.利用Banach空间的几何性质(p型或p阶光滑),在较弱的条件下得到了B值随机元序列加权和的强大数律,这些结果推广和改进了已知的一些文献中相应的结论.     

一类独立B值随机元的完全收敛性

本文讨论 B 值随机元的完全收敛性,将有关独立同分布随机元的完全收敛性的研究拓广到独立不同分布情形,同时将随机元单纯的矩条件过渡到选定的函数类 S 上.     

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。     

A Note on Complete Convergence for Arrays of Rowwise Independent Banach Space Valued Random Elements

We obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. Compared with similar results presented in the probabilistic literature our conditions are weaker.     

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.     

Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements

For a double array {V_(m,n), m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p(1 ≤ p ≤ 2) Banach space and an increasing double array {b_(m,n), m ≥1, n ≥ 1} of positive constants, the limit law ■ and in L_p as m∨n→∞ is shown to hold if ■ This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space.     

B值随机变量序列的一类局部收敛定理

研究取值于Banach空间随机变量序列的一类局部收敛定理．作为推论,得到了一类B值鞅差序列的极限定理和经典的独立随机变量序列的极限定理,     

On the Complete Convergence of Moving Average Process with Banach Space Valued Random Elements

Let {Y _i ;−∞<i<∞} be a doubly infinite sequence of independent random elements taking values in a separable real Banach space and stochastically dominated by a random variable X. Let {a _i ;−∞<i<∞} be an absolutely summable sequence of real numbers and set V _i =∑ _k=−∞^∞ a _i+k Y _i ,i≥1. In this paper, we derive that if and E|X| ^μ log  ^ρ |X|<0, for some μ (0<μ<2, μ≠1) and ρ>0 then for all ε>0. This work was partially supported by the Korean Research Foundation Grant funded by the Korean Government (KRF-2006-353-C00006, KRF-2006-251-C00026).