有界线性算子的不变性与拟鞅变换的局部收敛性  

INVARIANCE OF BOUNDED LINEAR OPERATORS AND LOCAL CONVERGENCE OF QUASI-MARTINGALE TRANSFORMS

作　　者：甘师信[1] 

机构地区：[1]武汉大学数学系

出　　处：《武汉大学学报（自然科学版）》1992年第1期1-10,共10页Journal of Wuhan University(Natural Science Edition)

基　　金：国家自然科学基金

摘　　要：设B与B′是两个实的Banach空间,f是B到B′的有界线性算子,X=(X_,F_,n≥1)是B值某种鞅型序列。本文证明了:X在有界线性算子变换下f(x)=(f(X_),F_,n≥1)的鞅型性质与某些积分性质不变。本文还给出了一些拟鞅变换局部收敛的结果,这些结果推广与改进了一些已知的结论。Let B and B' be any two real Banach spaces, f is a bounded linear operator from B to B'. X=(X_n, F_n, n>1) is a martingale-like sequence of some type. In this paper we prove that f(X)=(f(X_n), F_n, n≥1) remains a mart ingale-like sequence of the same type as X ard inherit some properties of integrals of X. In the other direction some results of local convergence of quasi-martingle transforms are given. Some known results are extended and proved.

关 键 词：有界线性算子 拟鞅变换 局部收敛 

分 类 号：O177.92[理学—数学]