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
$S_{n}=X_{1}+X_{2}+...+X_{n}$@. Denote
$lambda(varepsilon)=displaystylesum_{n=1}^{infty}P(|S_{n}|geq
nvarepsilon)$@. O.I. Klesov proved that if $EX_{1}=0$,
$EX_{1}^{2}=sigma ^{2}
eq 0$, $E|X_{1}|^{3}<infty$, then
$displaystylelim_{varepsilondownarrow0}varepsilon^{frac{3}{2}}(lambda(varepsilon)-frac{sigma^{2}}{varepsilon^{2}})=0$.
In this thesis, it is shown that if $EX_{1}=0$,
$EX_{1}^{2}=sigma ^{2}
eq 0$, $E|X_{1}|^{2+delta}<infty$ for
some $displaystyledeltain(frac{1}{2},1]$, then
$displaystylelim_{varepsilondownarrow0}varepsilon^{frac{3}{2}}(lambda(varepsilon)-frac{sigma^{2}}{varepsilon^{2}})=0$.
end{abstract}
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0624104-165707 |
| Date | 24 June 2004 |
| Creators | Chen, Tsung-Wei |
| Contributors | Chien-Sen Huang, Tsai-Lien Wong, Jhishen Tsay |
| 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-0624104-165707 |
| Rights | unrestricted, Copyright information available at source archive |
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