B值适应可积序列加权和的强收敛性  

Strong convergence of weighted sums with Banach space valued integrable adapter sequences

作　　者：万成高[1] 万英[1] 

机构地区：[1]湖北大学数学与计算机科学学院,湖北武汉430062

出　　处：《湖北大学学报（自然科学版）》2013年第3期370-374,共5页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(10571139)资助

摘　　要：设{Xn,Fn,n≥1}是B值适应可积序列(或B值鞅差序列),{an,n≥1}和{bn,n≥1}是两个正常数列,本文中研究了形如1/bn∑ni=1ai(Xi-E(Xi|Fi-1))或(1/bn∑ni=1aiXi)加权和的强收敛性,得到了一些适当条件下加权和的强收敛性的结果.We mainly studied the strong convergence of weighted sums of the form 1/bn∑n i=1ai（Xi-E（Xi｜Fi-1））（or1/bn∑n i=1aiXi）,where {Xn,Fn,n≥1} was an arbitrary Banach space valued integrable adapter sequence（or Banach space valued martingale difference） and {an,n≥1} and {bn,n≥1} were two sequences of positive constants.Some new strong convergence for such weighted sums were proved under mild conditions.

关 键 词：B值适应可积序列 B值鞅差序列 加权和 强收敛性 

分 类 号：O211.4[理学—概率论与数理统计]