NA阵列加权乘积和的完全收敛性

设{X_(ni):1≤i≤n,n≥1}为行间NA阵列,g(x)是R~+上指数为α的正则变化函数,r>0,m为正整数,{a_(ni):1≤i≤n,n≥1}为满足条件(?)|a_(ni)|=O((g(n))~1)的实数阵列,本文得到了使sum from n=1 to ∞n~(r-1)Pr(|■multiply from j=1 to m a_(nij) X_(nij)|>ε)<∞,■ε>0成立的条件,推广并改进了Stout及王岳宝和苏淳等的结论。     

m-NA随机阵列的完全收敛性的一个注记

本文研究了行m-NA随机阵列的完全收敛性.利用文[8]中结果获得了m-NA列最大部分和的一个概率不等式,并根据该不等式和截尾的方法,探讨了行m-NA随机阵列的完全收敛性,获得了与行NA随机阵列情形类似的结果,简化了文[5]中定理1的证明.     

可交换随机变量序列的完全收敛性

本文探讨了可交换随机变量的完全收敛性问题，从充性和必要性两方面都作了研究，并把ｉ．ｉ．ｄ．情形下的部分结果作了为特例推出。     

NA列加权乘积和的完全收敛性

本文讨论了NA和几类加权部分和及加权乘积和的完全收敛性，其中部分结果要优于iid列的已知结论。     

NA序列部分和的完全收敛性

本文讨论了非平稳NA随机变量序列部分和的完全收敛性,获得了一般形式的完全收敛速度与矩条件之间的等价关系,其结果与独立情形一致,从而证实了NA序列与独立序列有着极为类似的完全收敛性．     

混合序列加权和的强收敛性

本文给出混合序列加权和的强收敛性的一些充分条件，这些结论推广和改进了文［１］定理３，文［２］定理３；文［３］定理４．１５以及文［４］定理４．     

两两NQD列的大数定律和完全收敛性

本文主要研究了两两NQD列的的大数定律和完全收敛性,获得了与独立情形一样的大数定律和完全收敛定理.     

独立阵列和的最大值完全收敛的等价条件

本文得到了独立阵列和(含加权和)的最大值完全收敛的等价条件,从而丰富和强化了前人的结果．     

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。     

EQUIVALENCE OF COMPLETE CONVERGENCE AND LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS

1.IntroductionandMainResultsAsequence{X.,n21}ofrealvaluedrandomvariablesissaidtosatisfythelawoflargenumbersofHsu-Robbins(1947)typewithasequence{b.}ofrealnumbersifVP(ISn-b.I2ne)< co,Ve>0,(1.1)ZP(ISn-b.I2ne)< co,Ve>0,(1.1)n=1whereS.~ZXi.Conditionsunderwhich(1.1)holdswerediscussedinmanypapers.Ai=1moregeneralresultforlidrealvaluedrandomvariablesisgivenin[2].LetBbearealseparableBanachspacewithnorm11'11and{X.}asequenceofB-valuedrandomelemefltsandputSa~ZXi,n21.Candcdenotepositivefinitecon…     

两两NQD列的强收敛性

利用两两NQD列部分和矩不等式和截尾法,探讨了两两NQD列的完全收敛性和强大数定律,所获结论推广并改进了相关文献已有结果.     

关于任意随机可积序列的一个强收敛定理

本文研究了可积随机适应序列强收敛定理的问题.利用构造截尾停时以及鞅差序列的方法,获得了一类任意积随机适应序列的强收敛定理,推广了若干已知的结果.     

ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

It is well-known that the complete convergence theorem for i.i.d. random variables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ∈ goes to zero, so it is of interest to investigate the asymptotic behavior of the series as ∈ goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.     

EQUIVALENCE OF COMPLETE CONVERGENCE AND LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS＇

Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number forB- valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker. Project supported by the National Natural Science Foundation of China.     

CONVERGENCE RATES IN THE LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS

1 Introduction and Main ResultsLet {X.,n > 1} be a sequence of random variables in the same probability space andnput Sn = Z Xj, n 2 1. ln real-valued case1 the rates of convergence to zero of qualltitiesi = 1P(lS.I/n'/' > E) (0 < f < 2) are described by the well-known theorem of Baum and Katz(1965):Theorem BK Let 0 < t < 2,r 2 1, and let {X., n 2 1} be real valued iid r.v.'s, when1 5 t < 2, EXl = 0. ThenIn l985, Bai and Su generalized Theorem BK and obtained the correspondillg resul…     

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．     

一类非平稳高斯序列超过数点过程与和的渐近性

设{X_i}_(i=1)~∞是标准化非平稳高斯序列,N_n为X_1,X_2,…,X_n依次对水平μ_(n1),μ_(n2),…,μ_(nn)的超过数形成的点过程.记Υ_(ij)=X_iX_j,S_n=■X_i.当Υ_(ij)满足一定条件时,证明了N_n依分布收敛到Poisson过程,且N_n与S_n渐近独立.     

A NOTE OF CONVERGENCE RATES FOR SUMS OF ρ-MIXING SEQUENCES

1.IntroductionandMainResultSincethedefinitiononthecompleteconvergencewasintroducedbyHsuandRobbins[1],therehavebeenmanyauthorswhodevotethemselvestothestudyonthisconvergenceofiidrandomvariables,seeGut[2,3],BaiandSu[4]andLin[5].Meanwhile,somescholarshav...     

ON THE RATE OF CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS

1IntroductionConsiderthefollowingdifferenceequationwhereGfRxR-Riscontinuous,p:Z -R ,k;Z -Z ,p(n)5M,k(n)5k,MER ,kEZ ;ZandZ denotethesetsofintegersandnonnegativeintegers,respective1y.Forintegersaand5,a>6,wedefineZ(a,5)={a,a l,'',6},Z(a)={a,a l,'.}.Weassumethat(i)G(x,.)ismonotonenon-decreasing,(ii)G(.,y)ismonotonenon-increasing;(iii)G(x,x)=o,G(x,y)5oforx>yandG(x,y)2oforx相似文献   

A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers

We consider a new family of convex weakly compact valued integrable random sets which is called an adapted array of convex weakly compact valued integrable random variables of type p (1?p?2). By this concept, more general laws of large numbers will be established. Some illustrative examples are provided.