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}
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0612103-122350 |
| Date | 12 June 2003 |
| Creators | Tseng, Tzu-Hui |
| Contributors | ¨S¦³, ¨S¦³, ¨S¦³ |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612103-122350 |
| Rights | unrestricted, Copyright information available at source archive |
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