26887 articles – 20547 Notices  [english version]
Fiche détaillée Articles dans des revues avec comité de lecture
Annales de l'IHP - Probabilités et Statistiques 47, 3 (2011) 629-649
A nonasymptotic theorem for unnormalized Feynman-Kac particle models
Frédéric Cérou1, 2, Pierre Del Moral3, 4, 5, Arnaud Guyader2, 6

We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman-Kac models. We provide an original stochastic analysis-based on Feynman-Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the L(2)-relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first results of this type for this class of unnormalized models. We also illustrate these results in the context of particle absorption models, with a special interest in rare event analysis.
1 :  IRMAR - Institut de Recherche Mathématique de Rennes
3 :  INRIA Bordeaux - Sud-Ouest - ALEA
4 :  IMB - Institut de Mathématiques de Bordeaux
5 :  CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
6 :  MASS - Département Mathématiques appliquées et sciences sociales - Rennes 2
Processus stochastiques
Interacting particle systems – Feynman-Kac semigroups – Nonasymptotic estimates – Genetic algorithms – Boltzmann-Gibbs measures – Monte Carlo models – Rare events