B值混合随机变量的强大数定律(英文)

Strong Law of Large Numbers for B-Valued Mixing Random Variables

本文在Banach空间B是p可光滑(1<p≤2)的条件下获得了B值弱相依随机变量序列正则和极限点集的上界．作为应用,由B值y-混合随机变量序列的强大数定律刻划了Banach 空间的p可光滑性,在不要求混合系数(?)n和ψn趋于0而是在infn≥1(?)n=0或infn≥1ψn=0的条件下,获得了B值相依随机变量序列有关强大数定律的一些结果．

In this paper, we obtain the almost sure bound of normal sum of B-valued weakly dependent random variables under the assumption that Banach space B is p-smoothable （1 〈： p 〈： 2）. As its application, we characterize p-smoothness of Banach space through the strong law of large numbers of B-valued y-mixing random variables, and obtain some results on the strong law of large numbers for B-valued dependent random variables without assumption on rate of tending to zero of ψ and ψ-mixing parameters ψn and ψn but under the assumption that inf n≥1ψn=0 or inf n≥1ψn=0 respectively.