A NEW KIND OF THE LAW OF THE ITERATED LOGARITHM FOR PRODUCT OF A CERTAIN PARTIAL SUMS

Let {X, X-i; i >= 1} be a sequence of independent and identically distributed positive random variables. Denote S-n = Sigma(n)(i)=1 X-i and S-n((k)) = S-n - X-k for n >= 1, 1 <= k <= n. Under the assumption of the finiteness of the second moments, we derive a type of the law of the iterated logarithm for S the limit point set for its certain normalization.