ON LARGE DEVIATION PROBABILITIES FOR PROPERLYNORMALIZED WEIGHTED SUMS AND RELATED LAW OF ITERATED LOGARITHM

Let be a sequence of independent and identically distributed random variables withdistribution function F. When F belongs to the domain of attraction of a stable law with index α, 0 2 and α≠1, an asymptotic behaviour of the large deviation probabilities with respect to properly normalized weighted sums have been studied and in support of this we obtained Chover's form of law of iterated logarithm.