关于独立同分布正态随机变量部分和尾概率的注(英文)

A Remark on the Tail Probability Sums of i.i.d.Gaussian Random Variable

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=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε2λ(ε)-σ2+ε2 /2 ≤ C2ε3.

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=1Xk,EX2=σ2〉0,Sn=n∑k=1Xk,λ（ε）=∞∑n=1P（｜Sn｜≥nε）.In this paper,we prove that there exists positive constants C1and C2,for small enough ε〈0,it follows that C1ε3≤ε2λ（ε）-σ2＋ε2/2≤C2ε3.