Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 44, Number 4 (2012), 1173-1196.
Rare-event simulation of heavy-tailed random walks by sequential importance sampling and resampling
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.
Adv. in Appl. Probab., Volume 44, Number 4 (2012), 1173-1196.
First available in Project Euclid: 5 December 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 65C05: Monte Carlo methods
Secondary: 60G50: Sums of independent random variables; random walks
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