Subexponential distributions and integrated tails.

Let F be a distribution function on [0, oc) with finite expectation. In terms of the hazard rate of F several conditions are given which simultaneously imply subexponentiality of F and of its integrated tail distribution Fl. These conditions apply to a wide class of longtailed distributions, and they can also be used in connection with certain random walks which occur in risk theory and queueing theory. INTEGRATED TAIL DISTRIBUTION; SUBEXPONENTIALITY; DOMINATED VARIATION; RANDOM WALK THEORY; RISK THEORY; QUEUEING THEORY