Efficient Simulation for Large Deviation Probabilities of Sums of Heavy-Tailed Increments

Abstract

Let (Xn:n ges 0) be a sequence of iid rv's with mean zero and finite variance. We describe an efficient state-dependent importance sampling algorithm for estimating the tail of Sn = X1 + ... + Xn in a large deviations framework as n - infin. Our algorithm can be shown to be strongly efficient basically throughout the whole large deviations region as n - infin (in particular, for probabilities of the form P (Sn > kn) as k > 0). The techniques combine results of the theory of large deviations for sums of regularly varying distributions and the basic ideas can be applied to other rare-event simulation problems involving both light and heavy-tailed features