Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A NEW KIND OF THE LAW OF THE ITERATED LOGARITHM FOR PRODUCT OF A CERTAIN PARTIAL SUMS

  • Zang, Qing-Pei (School of mathematical science Huaiyin Normal University)
  • Received : 2010.03.26
  • Published : 2011.09.30
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Abstract

Let {X, $X_{i};\;i{\geq}1$} be a sequence of independent and identically distributed positive random variables. Denote $S_n= \sum\array\\_{i=1}^nX_i$ and $S\array\\_n^{(k)}=S_n-X_k$ for n ${\geq}$1, $1{\leq}k{\leq}n$. Under the assumption of the finiteness of the second moments, we derive a type of the law of the iterated logarithm for $S\array\\_n^{(k)}$ and the limit point set for its certain normalization.

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References

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