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URN etd-0612103-122350
Author Tzu-Hui Tseng
Author's Email Address m9024608@student.nsysu.edu.tw
Statistics This thesis had been viewed 5063 times. Download 2385 times.
Department Applied Mathematics
Year 2002
Semester 2
Degree Master
Type of Document
Language English
Title On the convergence rate of complete convergence
Date of Defense 2003-05-30
Page Count 10
Keyword
  • complete convergence
  • convergence rate
  • 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 $displaystyle S_{n}=X_{1}+X_{2} +cdots X_{n}$. 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}
    Advisory Committee
  • 沒有 - chair
  • 沒有 - co-chair
  • 沒有 - advisor
  • Files
  • etd-0612103-122350.pdf
  • indicate access worldwide
    Date of Submission 2003-06-12

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