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.
Publié le : 2000-04-14
Classification:
conditional Monte Carlo,
importance sampling,
large deviations,
logarithmic efficiency,
M/G/1 queue,
order statistics,
random walk,
regular variation,
subexponential distribution
@article{1081788030,
author = {Asmussen, S\o ren and Binswanger, Klemens and H\o jgaard, Bjarne},
title = {Rare events simulation for heavy-tailed distributions},
journal = {Bernoulli},
volume = {6},
number = {6},
year = {2000},
pages = { 303-322},
language = {en},
url = {http://dml.mathdoc.fr/item/1081788030}
}
Asmussen, Søren; Binswanger, Klemens; Højgaard, Bjarne. Rare events simulation for heavy-tailed distributions. Bernoulli, Tome 6 (2000) no. 6, pp. 303-322. http://gdmltest.u-ga.fr/item/1081788030/