From light tails to heavy tails through multiplier

摘要

Let X and Y be two independent nonnegative random variables, of which X has a distribution belonging to the class L(γ) or S(γ) for some γ ≥ 0 and Y is unbounded. We study how their product XY inherits the tail behavior of X. Under some mild technical assumptions we prove that the distribution of XY belongs to the class L(0) or S(0) accordingly. Hence, the multiplier Y builds a bridge between light tails and heavy tails.