| 关于独立同分布正态随机变量部分和尾概率的注(英文) |
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| 引用本文： | 何建军,谢庭藩.关于独立同分布正态随机变量部分和尾概率的注(英文)[J].应用概率统计,2012,28(3):277-284. |
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| 作者姓名： | 何建军 谢庭藩 |
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| 作者单位： | 中国计量学院数学系 |
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| 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=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.
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| 关 键 词： | 逼近速度 i.i.d.正态随机变量 尾概率 |
A Remark on the Tail Probability Sums of i.i.d.Gaussian Random Variable |
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| He Jianjun Xie Tingfan.A Remark on the Tail Probability Sums of i.i.d.Gaussian Random Variable[J].Chinese Journal of Applied Probability and Statisties,2012,28(3):277-284. |
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| Authors: | He Jianjun Xie Tingfan |
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| Institution: | Department of Mathematics, China Jiliang University |
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| Abstract: | Let be a sequence
of i.i.d. Gaussian random variables with zero mean and finite
variance, and set  ,
=\tsm_{n=1}^{\infty}\pr(|S_{n}|\geq n\epsilon)$) .
In this paper, we prove that there exists positive constants  and  ,
for small enough $\epsilon>0$, it follows that
 , it follows that
 -\sigma^{2}+{\epsilon^{2}}/{2}\leq C_{2}\epsilon^{3}$) . |
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| Keywords: | |
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