A Mean Field Theory of Nonlinear Filtering
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Advanced Learning Evolutionary Algorithms [ALEA] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| hal.structure.identifier | Laboratoire Jean Alexandre Dieudonné [JAD] | |
| dc.contributor.author | PATRAS, Frédéric | |
| hal.structure.identifier | Laboratoire Jean Alexandre Dieudonné [JAD] | |
| dc.contributor.author | RUBENTHALER, Sylvain | |
| dc.date.issued | 2008 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.subject.en | Feynman-Kac measures | |
| dc.subject.en | nonlinear filtering | |
| dc.subject.en | interacting particle systems | |
| dc.subject.en | historical and genealogical tree models | |
| dc.subject.en | central limit theorems | |
| dc.subject.en | Gaussian fields | |
| dc.subject.en | propagations of chaos | |
| dc.subject.en | trees and forests | |
| dc.subject.en | combinatorial enumeration | |
| dc.title.en | A Mean Field Theory of Nonlinear Filtering | |
| dc.type | Rapport | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| bordeaux.type.institution | INRIA | |
| bordeaux.type.report | rr | |
| hal.identifier | inria-00238398 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00238398v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2008&rft.au=DEL%20MORAL,%20Pierre&PATRAS,%20Fr%C3%A9d%C3%A9ric&RUBENTHALER,%20Sylvain&rft.genre=unknown |
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