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Rare-Event Simulation of Heavy-Tailed Random Walks by Sequential Importance Sampling and Resampling

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic processes

Published online by Cambridge University Press:  04 January 2016

Hock Peng Chan ,
Shaojie Deng  and
Tze-Leung Lai
Hock Peng Chan*
Affiliation:
National University of Singapore
Shaojie Deng
Affiliation:
Microsoft
Tze-Leung Lai*
Affiliation:
Stanford University
*
∗ Postal address: Department of Statistics and Applied Probability, National University of Singapore, Science Drive 1, 119260, Singapore.
∗∗ Postal address: Statistics Department, Stanford University, Stanford, CA 94305, USA.
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Abstract

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We introduce a new approach to simulating rare events for Markov random walks with heavy-tailed increments. This approach involves sequential importance sampling and resampling, and uses a martingale representation of the corresponding estimate of the rare-event probability to show that it is unbiased and to bound its variance. By choosing the importance measures and resampling weights suitably, it is shown how this approach can yield asymptotically efficient Monte Carlo estimates.

Keywords

Efficient simulationheavy-tailed distributionsequential Monte Carloregularly varying tail

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60G50: Sums of independent random variables; random walks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 4 , December 2012 , pp. 1173 - 1196
Copyright
© Applied Probability Trust 

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