Banach空间随机元的强极限定理

Strong Limit Theorems of Random Elements on Banach Space

Hanson等人得出了如下两个结果: 定理A 设{X,Xn;n≥1)是独立同分布的实随机变量序列,EX=μ,m（θ）=EeOX对某个含μ的开区间是有限的,{tn;n≥1}是一个正整数序列且tn≤n（n≥1）,tn/1gn→∞。

Let B be a separable Banach space and {X_n} a sequence of i. i. d. B-valued random elements with EX_1=0, and {t_n} a nondecreasing sequence of positive integers such that t_n≤n. We consider the problem: (?) (1/k)‖S_n-S_(n-k)‖→0 a. s., Hanson and Russo had given the results in [1] when B=R^1. This paper explores the versidn of [1] in the Banach space setting by using of theory of large deviations.