DEL MORAL, Pierre; PATRAS, Frédéric; RUBENTHALER, Sylvain

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

PATRAS, Frédéric
Laboratoire Jean Alexandre Dieudonné [JAD]

RUBENTHALER, Sylvain
Laboratoire Jean Alexandre Dieudonné [JAD]

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Ce document a été publié dans

The Oxford Handbook of Nonlinear Filtering, The Oxford Handbook of Nonlinear Filtering. 2011p. 705-740

Oxford University Press

Résumé en anglais

We present a mean field particle theory for the numerical approximation of Feynman-Kac path integrals in the context of nonlinear filtering. We show that the conditional distribution of the signal paths given a series of noisy and partial observation data is approximated by the occupation measure of a genealogical tree model associated with mean field interacting particle model. The complete historical model converges to the McKean distribution of the paths of a nonlinear Markov chain dictated by the mean field interpretation model. We review the stability properties and the asymptotic analysis of these interacting processes, including fluctuation theorems and large deviation principles. We also present an original Laurent type and algebraic tree-based integral representations of particle block distributions. These sharp and non asymptotic propagations of chaos properties seem to be the first result of this type for mean field and interacting particle systems.< Réduire

Mots clés en anglais

Feynman-Kac measures

nonlinear filtering

interacting particle systems

historical and genealogical tree models

central limit theorems

Gaussian fields

propagations of chaos

trees and forests

combinatorial enumeration

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251