p-型空间与B值随机元和尾概率的收敛速度

p-TYPE SPACE AND CONVERGENCE RATES OF TAIL PROBABILITIES FOR SUMS OF B-VALUED RANDOM ELEMENTS

本文讨论了B值随机元非随机足标与随机足标和尾概率的收敛速度．借助于B值独立随机元序列满足强大数定律与弱大数定律等价的这一特性，得到了Banach空间p型性质的刻划，同时将［1，2］中实值独立同分布随机变量和完全收敛性的相应结果推广到B值独立但不必同分布情形．其中，0＜t＜1时，去掉了对随机无独立性的要求．

We discuss in this paper convergence rates of tail probabilties for partial sumsand randomly indexed partial sums of B-valued random elements. By the equivalent property of strong and weak law of large numbers of B-valued independent random elements,we obtain the characterization of p--type Banach space in teams of the convergence rates forsums of zero mean B--valued independent random elements. The corresponding results in[1,2] on i.i.d. real random variables are extended to the case of B-valued independent but notnecessary identically distributed random elements, and when 0 < t < 1, the independenceon random elements is eliminated.