A non asymptotic variance theorem for unnormalized Feynman-Kac particle models

Frédéric Cérou 1 Pierre del Moral 2, 3, 4 Arnaud Guyader 1, 5
1 ASPI - Applications of interacting particle systems to statistics
UR1 - Université de Rennes 1, Inria Rennes – Bretagne Atlantique , CNRS - Centre National de la Recherche Scientifique : UMR6074
2 A3 - Advanced analysis to code optimization
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France
4 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
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Submitted on : Thursday, November 6, 2008 - 6:39:50 PM
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Frédéric Cérou, Pierre del Moral, Arnaud Guyader. A non asymptotic variance theorem for unnormalized Feynman-Kac particle models. [Research Report] RR-6716, INRIA. 2008. ⟨inria-00337392⟩

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