Genetic genealogical models in rare event analysis

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 DGAC - Direction Générale de l'Aviation Civile

We present in this article a genetic type interacting particle systems algorithm and a genealogical model for estimating a class of rare events arising in physics and network analysis. We represent the distribution of a Markov process hitting a rare target in terms of a Feynman-Kac model in path space. We show how these branching particle models described in previous works can be used to estimate the probability of the corresponding rare events as well as the distribution of the process in this regime.

Domaines: Probabilités [math.PR]

Frédéric Cérou, Pierre del Moral, François Le Gland, Pascal Lezaud. Genetic genealogical models in rare event analysis. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2006, 1, pp.181--203. ⟨hal-00912022⟩