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

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2 Author(s)
Blanchet, J.H. ; Dept. of Stat., Harvard Univ., Cambridge, MA ; Jingchen Liu

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

Published in:

Simulation Conference, 2006. WSC 06. Proceedings of the Winter

Date of Conference:

3-6 Dec. 2006