A non asymptotic variance theorem for unnormalized Feynman-Kac particle models
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.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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