A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals

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 propose a new approach to study the stability of the optimal filter w.r.t. its initial condition, by introducing a "robust" filter, which is exponentially stable and which approximates the optimal filter uniformly in time. The "robust" filter is obtained here by truncation of the likelihood function, and the robustification result is proved under the assumption that the Markov transition kernel satisfies a pseudo-mixing condition (weaker than the usual mixing condition), and that the observations are "sufficiently good". This robustification approach allows us to prove also the uniform convergence of several particle approximations to the optimal filter, in some cases of nonergodic signals.
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Stochastic Processes and their Applications, Elsevier, 2003, 106 (2), pp.279-316. 〈10.1016/S0304-4149(03)00041-3〉
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https://hal.inria.fr/hal-00912082
Contributeur : Francois Le Gland <>
Soumis le : dimanche 1 décembre 2013 - 23:21:22
Dernière modification le : mercredi 16 mai 2018 - 11:23:05

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François Le Gland, Nadia Oudjane. A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals. Stochastic Processes and their Applications, Elsevier, 2003, 106 (2), pp.279-316. 〈10.1016/S0304-4149(03)00041-3〉. 〈hal-00912082〉

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