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

Sören Asmussen

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingResearchpeer-review

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
Original languageEnglish
Title of host publicationMonte-Carlo and Quasi-Monte Carlo Methods 2000. Proceedings of a Conference
PublisherSpringer
Pages1-9
ISBN (Print)3-540-42718-X
Publication statusPublished - 2002
EventProceedings of Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing - Hong Kong, China
Duration: 2000 Nov 272000 Dec 1

Conference

ConferenceProceedings of Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing
Country/TerritoryChina
CityHong Kong
Period2000/11/272000/12/01

Subject classification (UKÄ)

  • Probability Theory and Statistics

Keywords

  • conditional distribution
  • heavy-tailed distributions
  • importance sampling
  • rare event
  • small probabilities
  • rare events simulation

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