A new kind of the law of the iterated logarithm for product of a certain partial sums
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 1041-1046
https://doi.org/10.4134/BKMS.2011.48.5.1041
Printed September 1, 2011
Qing-Pei Zang
Huaiyin Normal University
Abstract : Let $\{X,~X_{i};~i\geq1\}$ be a sequence of independent and identically distributed positive random variables. Denote $S_{n}=\sum_{i=1}^{n}X_{i}$ and $S_{n}^{(k)}=S_{n}-X_{k}$ for $n\geq1$, $1\leq k\leq n$. Under the assumption of the finiteness of the second moments, we derive a type of the law of the iterated logarithm for $S_{n}^{(k)}$ and the limit point set for its certain normalization.
Keywords : law of the iterated logarithm, product of partial sums, strong law of large numbers
MSC numbers : 60F15
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