Infinite divisibility and generalized subexponentiality

Abstract

We introduce a new class of distributions by generalizing the subexponential class to investigate the asymptotic relation between the tails of an infinitely divisible distribution and its Lévy measure. We call a one-sided distribution μ O-subexponential if it has positive tail satisfying lim supx→∞ * μ(x, ∞)/μ(x, ∞)