SMALL DEVIATION PROBABILITIES FOR A WEIGHTED SUM OF INDEPENDENT POSITIVE RANDOM VARIABLES WITH COMMON DISTRIBUTION FUNCTION THAT CAN DECREASE AT ZERO FAST ENOUGH

摘要

The present note puts forward the most general conditions to date under which the classical asymptotics of the small deviation probabilities for a weighted sum of independent positive random variables takes place. Regarding random variables it is assumed that their common distribution function can, in particular, have an exponential falloff at zero.