inria-00337392, version 1
A non asymptotic variance theorem for unnormalized Feynman-Kac particle models
Frédéric Cérou
a, 1Pierre Del Moral 2, 3, 4Arnaud Guyader b, 1, 5
N° RR-6716 (2008)
Résumé : We present a non asymptotic 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 $\LL_2$-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 simulation of static Boltzmann-Gibbs measures and restricted distributions, with a special interest in rare event analysis.
- a – INRIA
- b – Université Rennes 2 - Haute Bretagne
- 1 : ASPI (INRIA - IRISA)
- CNRS : UMR6074 – INRIA – Université de Rennes 1
- 2 : A3 (INRIA Futurs)
- INRIA – Université Paris XI - Paris Sud
- 3 : Institut de Mathématiques de Bordeaux (IMB)
- CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
- 4 : CQFD (INRIA Bordeaux - Sud-Ouest)
- INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR5251
- 5 : Institut de Recherche Mathématique de Rennes (IRMAR)
- CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II
- Domaine : Mathématiques/Probabilités
- Référence interne : RR-6716
- inria-00337392, version 1
- http://hal.inria.fr/inria-00337392
- oai:hal.inria.fr:inria-00337392
- Contributeur : Frederic Cerou
- Soumis le : Jeudi 6 Novembre 2008, 18:39:50
- Dernière modification le : Jeudi 24 Février 2011, 16:57:13
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