SOME RECENT RESULTS IN RARE EVENT ESTIMATION

This article presents several state-of-the-art Monte Carlo methods for simulating and estimating rare events. A rare event occurs with a very small probability, but its occurrence is important enough to justify an accurate study. Rare event simulation calls for specific techniques to speed up standard Monte Carlo sampling, which requires unacceptably large sample sizes to observe the event a sucient number of times. Among these variance reduction methods, the most prominent ones are Importance Sampling (IS) and Multilevel Splitting, also known as Subset Simulation. This paper oers some recent results on both aspects, motivated by theoretical issues as well as by applied problems. Resume. Cet article propose un etat de l'art de plusieurs methodes Monte Carlo pour l'estimation d'evenements rares. Un evenement rare est par definition un evenement de probabilite tres faible, mais d'importance pratique cruciale, ce qui justifie une etude precise. La methode Monte Carlo classique s'averant prohibitivement couteuse, il importe d'appliquer des techniques specifiques pour leur estima- tion. Celles-ci se divisent en deux grandes categories : echantillonnage preferentiel d'un cote, methodes multi-niveaux de l'autre. Nous presentons ici quelques resultats recents dans ces domaines, motives par des considerations tant pratiques que theoriques.

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