EFFICIENT SIMULATION FOR LARGE DEVIATI

Let (Xn: n ≥ 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 ր ∞. Our algorithm can be shown to be strongly efficient basically throughout the whole large deviations region as n ր ∞ (in particular, for probabilities of the form P (Sn> κn) as κ> 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.