Stability and uniform approximation of nonlinear filters using the Hilbert metric, and application to particle filters

François Le Gland 1 Nadia Oudjane 2
1 SIGMA2 - Signal, models, algorithms
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective metric. These stability results are then used to prove, under some mixing assumption, the uniform convergence to the optimal filter of several particle filters, such as the interacting particle filter and some other original particle filters.
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The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2004, 14 (1), pp.144-187. 〈10.1214/aoap/1075828050〉
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Contributeur : Francois Le Gland <>
Soumis le : dimanche 1 décembre 2013 - 23:19:29
Dernière modification le : mercredi 16 mai 2018 - 11:23:05

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François Le Gland, Nadia Oudjane. Stability and uniform approximation of nonlinear filters using the Hilbert metric, and application to particle filters. The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2004, 14 (1), pp.144-187. 〈10.1214/aoap/1075828050〉. 〈hal-00912081〉

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