Open Access
April 2000 Rare events simulation for heavy-tailed distributions
Søren Asmussen, Klemens Binswanger, Bjarne Højgaard
Author Affiliations +
Bernoulli 6(2): 303-322 (April 2000).


This paper studies rare events simulation for the heavy-tailed case, where some of the underlying distributions fail to have the exponential moments required for the standard algorithms for the light-tailed case. Several counterexamples are given to indicate that in the heavy-tailed case, there are severe problems with the approach of developing limit results for the conditional distribution given the rare event; this is used as a basis for importance sampling. On the positive side, two algorithms having a relative error which is almost bounded are presented, one based upon order statistics and the other upon a different importance sampling idea.


Download Citation

Søren Asmussen. Klemens Binswanger. Bjarne Højgaard. "Rare events simulation for heavy-tailed distributions." Bernoulli 6 (2) 303 - 322, April 2000.


Published: April 2000
First available in Project Euclid: 12 April 2004

zbMATH: 0958.65010
MathSciNet: MR2001G:60226

Keywords: conditional Monte Carlo , importance sampling , large deviations , logarithmic efficiency , M/G/1 queue , order statistics , Random walk , regular variation , subexponential distribution

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability

Vol.6 • No. 2 • April 2000
Back to Top