設${X_{n}}^{infty}_{n=1}$為獨立且具有共同分怖之隨機變數，令$displaystyle
S_{n}=sum^{n}_{k=1}X_{k}$。定義
$displaystylelambda(varepsilon)=sum^{infty}_{n=1}P{left|S_{n}
ight|geq
nvarepsilon}$，本文主要來探討 $lambda(varepsilon)$
的收斂速度。 O.I. Klesov 證得如果 $E|X_{1}|^{3}$存在，則
$displaystyle
varepsilon^{frac{3}{2}}(lambda(varepsilon)-frac{sigma^{2}}{varepsilon^{2}})
ightarrow
0$。 這篇論文，我們得到如果對任意 $displaystyle
deltain(frac{sqrt{7}-1}{3},1]$， $E|X_{1}|^{2+delta}$都存在 ； 則
O.I. Klesov 所證得的結果仍然成立。

egin{abstract}
hspace{1cm}Let $X_{1}$, $X_{2}$, $cdots$, $X_{n}$ be a sequence
of independent indentically distributed random variables ( i. i.
d.) and $displaystyle S_{n}=X_{1}+X_{2} +cdots X_{n}$. Denote
$displaystylelambda(varepsilon)=sum^{infty}_{n=1}P{left|S_{n}
ight|geq
nvarepsilon}$, the convergence rate of
$displaystylelambda(varepsilon)$ is studied. O.I. Klesov proved
that if $E|X_{1}|^{3}$ exists, then $displaystyle
varepsilon^{frac{3}{2}}(lambda(varepsilon)-frac{sigma^{2}}{varepsilon^{2}})
ightarrow 0$.
In this thesis, we show that if $E|X_{1}|^{2+delta}<infty$ for
some $displaystyle
deltain(frac{sqrt{7}-1}{3},1]$, the result of O.I. Klesov
still holds.
end{abstract}

1. Introduction -------------1

2. Main result -------------4

3. Reference -------------10

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