A Mean field theory of nonlinear filtering
DEL MORAL, Pierre
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
DEL MORAL, Pierre
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Chapitre d'ouvrage
This item was published in
The Oxford Handbook of Nonlinear Filtering, The Oxford Handbook of Nonlinear Filtering. 2011p. 705-740
Oxford University Press
English Abstract
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 ...Read more >
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.Read less <
English Keywords
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
Origin
Hal imported