COMPARISON THEOREMS FOR SMALL DEVIATIONS OF WEIGHTEDSERIES

Leonid V. Rozovsky

Abstract: weighted series and obtain more refined versions of the known comparison results. In
particular, the following consequence is obtained immediately from Theorem 2.1 of the
paper.

Let a positive random variable belong to the domain of attraction of a stable law with
an index greater than one and let its distribution function be regularly varying at zero with
an exponent . If are independent copies of , and and
are positive summable sequences such that then as