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http://dx.doi.org/10.4134/BKMS.2011.48.5.1041

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.5, 2011 , pp. 1041-1046 More about this Journal
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.
Keywords
law of the iterated logarithm; product of partial sums; strong law of large numbers;
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