CÉROU, Frédéric; DEL MORAL, Pierre; GUYADER, Arnaud

doi:10.1214/10-AIHP358

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CÉROU, Frédéric
Applications of interacting particle systems to statistics [ASPI]
Institut de Recherche Mathématique de Rennes [IRMAR]

DEL MORAL, Pierre
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]

GUYADER, Arnaud
Applications of interacting particle systems to statistics [ASPI]
Département Mathématiques appliquées et sciences sociales - Rennes 2 [MASS]

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Este ítem está publicado en

Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2011, vol. 47, n° 3, p. 629-649

Institut Henri Poincaré (IHP)

Resumen en inglés

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.< Leer menos

Palabras clave en inglés

Interacting particle systems

Feynman-Kac semigroups

Nonasymptotic estimates

Genetic algorithms

Boltzmann-Gibbs measures

Monte Carlo models

Rare events

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A nonasymptotic theorem for unnormalized Feynman-Kac particle models

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