Branching and interacting particle interpretations of rare event probabilities

Pierre del Moral (1) , Pascal Lezaud (2)

1 UNS - Université Nice Sophia Antipolis (1965 - 2019)
2 DGAC - Direction Générale de l'Aviation Civile

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.

Domaines: Probabilités [math.PR]

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⟩