DEL MORAL, Pierre; MICLO, Laurent

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DEL MORAL, Pierre
Laboratoire Jean Alexandre Dieudonné [JAD]

MICLO, Laurent
Laboratoire d'Analyse, Topologie, Probabilités [LATP]

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Ce document a été publié dans

Stoch. Anal. Appl. 2007, vol. 25, n° 3, p. 519-575

Résumé en anglais

Recently we have introduced Moran type interacting particle systems in order to numerically compute normalized continuous time Feynman-Kac formulae. These schemes can also be seen as approximating procedures for certain simple generalized spatially homogeneous Boltzmann equations, so strong propagation of chaos is known to hold for them. We will give a new proof of this result by studying the evolution of tensorized empirical measures and then applying two straightforward coupling arguments. The only difficulty is in the first step to find nice martingales, and this will be done via the introduction of another family of Moran semigroups. This work also procures us the opportunity to present an appropriate abstract setting, in particular without any topological assumption on the state space, and to apply a genealogical algorithm for the smoothing problem in nonlinear filtering context.< Réduire

Mots clés en anglais

genealogical processes and smoothing problems in nonlinear filtering

Feynman-Kac formulae

perturbations of general Markov processes by jump bounded generators

interacting particle systems

weak and strong propagation of chaos

tensorized empirical measures

Moran semigroups and martingales

coupling

genealogical processes and smoothing problems in nonlinear filtering.

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251