Advances in Applied Probability

Rare-event simulation of heavy-tailed random walks by sequential importance sampling and resampling


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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.

Article information

Adv. in Appl. Probab., Volume 44, Number 4 (2012), 1173-1196.

First available in Project Euclid: 5 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65C05: Monte Carlo methods
Secondary: 60G50: Sums of independent random variables; random walks

Efficient simulation heavy-tailed distribution sequential Monte Carlo regularly varying tail


CHAN, HOCK PENG; DENG, SHAOJIE; LAI, TZE-LEUNG. Rare-event simulation of heavy-tailed random walks by sequential importance sampling and resampling. Adv. in Appl. Probab. 44 (2012), no. 4, 1173--1196. doi:10.1239/aap/1354716593.

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