Title page for etd-0624104-165707


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URN etd-0624104-165707
Author Tsung-Wei Chen
Author's Email Address chentw@math.nsysu.edu.tw
Statistics This thesis had been viewed 5062 times. Download 1960 times.
Department Applied Mathematics
Year 2003
Semester 2
Degree Master
Type of Document
Language English
Title On the Convergence Rate in a Theorem of Klesov
Date of Defense 2004-05-28
Page Count 12
Keyword
  • convergence rate
  • complete convergence
  • Abstract 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}
    Advisory Committee
  • Tsai-Lien Wong - chair
  • Chien-Sen Huang - co-chair
  • Jhishen Tsay - advisor
  • Files
  • etd-0624104-165707.pdf
  • indicate access worldwide
    Date of Submission 2004-06-24

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