B值随机元的和的尾概率及其收敛速度

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

§1.引言及主要结果 设B是一可分Banach空间,‖·‖表示其上的范数,{X_n}是定义在同一概率空间上的B值随机元序列,S_n=sum from n=1 to n X_k(在本文以下内容中,均使用这一记号,始终不变),{t_n}是单调不减的正实数序列,并且本文的目的是研究概率的收敛速度问题,其中ε为任一给定的正数。

Let{X_n}be a sequence of independent random elements in a separable Banach space B, and {t_n}a nondecreasing sequence of positive real numbers such that t_n→∞ as n→→∞. The present paper investigates the convergence rates for probabilities where ε is an arbitrary but fixed positive number. As an application we obtain some results on the convergence rates for tail probabilities for randomly indexed partial sums.