inria-00070307, version 1

## Adaptive multilevel splitting for rare event analysis

Frédéric Cérou () a1, Arnaud Guyader () b1

N° RR-5710 (2005)

Résumé : The estimation of rare event probability is a crucial issue in areas such as reliability, telecommunications, aircraft management. In complex systems, analytical study is out of question and one has to use Monte Carlo methods. When rare is really rare, which means a probability less than $10^-9$, naive Monte Carlo becomes unreasonable. A widespread technique consists in multilevel splitting, but this method requires enough knowledge about the system to decide where to put the levels at hand. This is unfortunately not always possible. In this paper, we propose an adaptive algorithm to cope with this problem: the estimation is asymptotically consistent, costs just a little bit more than classical multilevel splitting and has the same efficiency in terms of asymptotic variance. In the one dimensional case, we prove rigorously the a.s. convergence and the asymptotic normality of our estimator, with the same variance as with other algorithms that use fixed crossing levels. In our proofs we mainly use tools from the theory of empirical processes, which seems to be quite new in the field of rare events.

• a –  INRIA
• b –  Université Rennes 2 - Haute Bretagne
• 1 :  ASPI (INRIA - IRISA)
• CNRS : UMR6074 – INRIA – Université de Rennes 1
• Domaine : Informatique/Autre
• Mots-clés : RARE EVENTS / ADAPTIVE MULTILEVEL SIMULATION / ASYMPTOTIC NORMALITY
• Référence interne : RR-5710

• inria-00070307, version 1
• oai:hal.inria.fr:inria-00070307
• Contributeur :
• Soumis le : Vendredi 19 Mai 2006, 20:00:01
• Dernière modification le : Jeudi 18 Janvier 2007, 12:28:34