A nonasymptotic theorem for unnormalized Feynman-Kac particle models

Frédéric Cérou; Pierre Del Moral; Arnaud Guyader

hal-00688479, version 1

A nonasymptotic theorem for unnormalized Feynman-Kac particle models

Frédéric Cérou () ^1, 2, Pierre Del Moral () ^3, 4, 5, Arnaud Guyader () ^1, 6

Annales de l'IHP - Probabilités et Statistiques 47, 3 (2011) 629-649

Abstract: 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: ASPI (INRIA - IRISA)
INRIA – Université de Rennes 1 – Université de Rennes II - Haute Bretagne
2: Institut de Recherche Mathématique de Rennes (IRMAR)
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
3: ALEA (INRIA Bordeaux - Sud-Ouest)
INRIA – Université de Bordeaux – CNRS : UMR5251
4: Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
5: Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
Polytechnique - X – CNRS : UMR7641
6: Département Mathématiques appliquées et sciences sociales - Rennes 2 (MASS)
Université de Rennes II - Haute Bretagne

hal-00688479, version 1
http://hal.archives-ouvertes.fr/hal-00688479
oai:hal.archives-ouvertes.fr:hal-00688479
From: Marie-Annick Guillemer <>
Submitted on: Tuesday, 17 April 2012 17:11:33
Updated on: Tuesday, 11 September 2012 11:54:54

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DOI: 10.1214/10-AIHP358

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