Limit theorems for the multilevel splitting algorithm in the simulation of rare events

Frédéric Cérou (1) , Pierre del Moral (2) , François Le Gland (1) , Pascal Lezaud (3)

1 ASPI - Applications of interacting particle systems to statistics
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 CENA - Centre d'études de la Navigation Aérienne

In this article, a genetic-type algorithm based on interacting particle systems is presented, together with a genealogical model, for estimating a class of rare events arising for instance in telecommunication networks, nuclear engineering, etc. The distribution of a Markov process hitting a rare but critical set is represented in terms of a Feynman-Kac model in path space. Approximation results obtained previously for these models are applied here to estimate the probability of the rare events as well as the probability distribution of the critical trajectories.

Domaines: Probabilités [math.PR]

Frédéric Cérou, Pierre del Moral, François Le Gland, Pascal Lezaud. Limit theorems for the multilevel splitting algorithm in the simulation of rare events. Proceedings of the 2005 Winter Simulation Conference, Orlando 2005, Dec 2005, Orlando, United States. pp.682-691, ⟨10.1109/WSC.2005.1574309⟩. ⟨hal-00912039⟩