Advances in Applied Probability

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

HOCK PENG CHAN, SHAOJIE DENG, and TZE-LEUNG LAI

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Abstract

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

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

Dates
First available in Project Euclid: 5 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1354716593

Digital Object Identifier
doi:10.1239/aap/1354716593

Mathematical Reviews number (MathSciNet)
MR3052853

Zentralblatt MATH identifier
1269.65011

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

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

Citation

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. https://projecteuclid.org/euclid.aap/1354716593


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