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Large deviations in rare events simulation: examples, counterexamples and alternatives

Asmussen, Sören LU (2002) Proceedings of Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing p.1-9
Abstract
When simulating small probabilities, say of order 10<sup>-6</sup> or less, by importance sampling, an established principle is to choose the importance sampling distribution as close to the conditional distribution given the rare event as possible. Implementing this often leads into large deviations calculations and exponential change of measure. We survey some of the standard examples where this approach works and supplement existing counterexamples with new ones. Difficulties often arise as consequence of reflecting barriers and we present an algorithm which at least in simple cases is able to deal with this problem. Also the case of heavy-tailed distributions is considered
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
conditional distribution, heavy-tailed distributions, importance sampling, rare event, small probabilities, rare events simulation
host publication
Monte-Carlo and Quasi-Monte Carlo Methods 2000. Proceedings of a Conference
pages
1 - 9
publisher
Springer
conference name
Proceedings of Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing
conference location
Hong Kong, China
conference dates
2000-11-27 - 2000-12-01
external identifiers
  • wos:000175526000001
ISBN
3-540-42718-X
language
English
LU publication?
yes
id
5ac57197-1d73-417a-9ea2-2fe7392cf67e (old id 611224)
date added to LUP
2016-04-04 10:47:27
date last changed
2018-11-21 21:00:47
@inproceedings{5ac57197-1d73-417a-9ea2-2fe7392cf67e,
  abstract     = {When simulating small probabilities, say of order 10&lt;sup&gt;-6&lt;/sup&gt; or less, by importance sampling, an established principle is to choose the importance sampling distribution as close to the conditional distribution given the rare event as possible. Implementing this often leads into large deviations calculations and exponential change of measure. We survey some of the standard examples where this approach works and supplement existing counterexamples with new ones. Difficulties often arise as consequence of reflecting barriers and we present an algorithm which at least in simple cases is able to deal with this problem. Also the case of heavy-tailed distributions is considered},
  author       = {Asmussen, Sören},
  booktitle    = {Monte-Carlo and Quasi-Monte Carlo Methods 2000. Proceedings of a Conference},
  isbn         = {3-540-42718-X},
  language     = {eng},
  pages        = {1--9},
  publisher    = {Springer},
  title        = {Large deviations in rare events simulation: examples, counterexamples and alternatives},
  year         = {2002},
}