Branching and interacting particle interpretations of rare event probabilities

Pierre del Moral 1 Pascal Lezaud 2
1 UNS - Université Nice Sophia Antipolis
2 DGAC - Direction Générale de l'Aviation Civile
Abstract : This article focuses on branching particle interpretations of rare events. We connect importance sampling techniques with interacting particle algorithms, and multi-splitting branching models. These Monte Carlo methods are illustrated with a variety of examples arising in particle trapping analysis, as well as in ruin type estimation problems. We also provide a rather detailed presentation of the asymptotic theory of these particle algorithms, including exponential extinction probabilities, Lp-mean error bounds, central limit theorem, and fluctuation variance comparaisons.
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Submitted on : Tuesday, April 1, 2014 - 2:43:11 PM
Last modification on : Monday, February 19, 2018 - 4:42:01 PM

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Pierre del Moral, Pascal Lezaud. Branching and interacting particle interpretations of rare event probabilities. Stochastic Hybrid Systems, Springer, pp 277-323, 2006, Lecture Notes in Control and Information Science, Volume 337, Print ISBN : 978-3-540-33466-8 ; Online ISBN : 978-3-540-33467-5. ⟨10.1007/11587392_9⟩. ⟨hal-00968737⟩

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