关于独立同分布正态随机变量部分和尾概率的注

摘要

设{X,Xn,n ≥ 1}是独立同分布正态随机变量序列,EX=0且EX2=σ2＞0,Sn=n∑k=1Xk,λ(∈)=8∑n=P(|Sn|≥n∈)在本文中,我们证明了存在正常数C1和C2,使得对足够小的∈＞0,成立下列不等式C1∈3≤∈2λ(∈) -σ2+∈2/2≤C2∈3.%Let {X,Xn,n ≥ 1} be a sequence of i.i.d.Gaussian random variables with zero mean and finite variance,and set Sn =n∑k=1 Xk,EX2 =σ2 ＞ 0,λ(∈) =8∑n=P(|Sn| ≥ he).In this paper,we n=lprove that there exists positive constants C1 and C2,for small enough ∈ ＞ 0,it follows that C1∈3 ≤∈2λ(∈) - σ2 + ∈2/2 ≤ C2∈3.