On Importance Sampling with Mixtures for Random Walks with Heavy Tails
2012 (English)In: ACM Transactions on Modeling and Computer Simulation, ISSN 1049-3301, Vol. 22, no 2, 8- p.Article in journal (Refereed) Published
State-dependent importance sampling algorithms based on mixtures are considered. The algorithms are designed to compute tail probabilities of a heavy-tailed random walk. The increments of the random walk are assumed to have a regularly varying distribution. Sufficient conditions for obtaining bounded relative error are presented for rather general mixture algorithms. Two new examples, called the generalized Pareto mixture and the scaling mixture, are introduced. Both examples have good asymptotic properties and, in contrast to some of the existing algorithms, they are very easy to implement. Their performance is illustrated by numerical experiments. Finally, it is proved that mixture algorithms of this kind can be designed to have vanishing relative error.
Place, publisher, year, edition, pages
2012. Vol. 22, no 2, 8- p.
Rare event simulation, heavy tails, importance sampling
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-11269DOI: 10.1145/2133390.2133392ISI: 000302131400002ScopusID: 2-s2.0-84859453675OAI: oai:DiVA.org:kth-11269DiVA: diva2:271897
FunderSwedish Research Council, 621-2008-4944
QC 201008112009-10-132009-10-132012-05-03Bibliographically approved