Bulletin of the
Korean Mathematical Society BKMS

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