DEL MORAL, Pierre; DOUCET, Arnaud; SINGH, Sumeetpal

doi:10.1051/m2an/2010048

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DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]

DOUCET, Arnaud
Dept of Statistics & Dept of Computer Science

SINGH, Sumeetpal
Cavendish Laboratory

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Article de revue

Ce document a été publié dans

ESAIM: Mathematical Modelling and Numerical Analysis. 2010, vol. 44, n° 5, p. 947-975

EDP Sciences

Résumé en anglais

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals on-the-fly as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results w.r.t. the time horizon parameter as well as functional central limit theorems and exponential concentration estimates, yielding what seems to be the first results of this type for this class of models. We also illustrate these results in the context of computational physics and imaginary time Schroedinger type partial differential equations, with a special interest in the numerical approximation of the invariant measure associated to h-processes.< Réduire

Mots clés en anglais

non asymptotic estimates

Feynman-Kac models

mean field particle algorithms

functional central limit theorems

exponential concentration

non asymptotic estimates.

DOI

http://dx.doi.org/10.1051/m2an/2010048

Project ANR

Sécurité et fiabilité des techniques de tatouages - ANR-06-SETI-0009

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251