The Annals of Applied Probability

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

François Le Gland and Nadia Oudjane

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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.

Article information

Ann. Appl. Probab., Volume 14, Number 1 (2004), 144-187.

First available in Project Euclid: 3 February 2004

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Zentralblatt MATH identifier

Primary: 93E11: Filtering [See also 60G35] 93E15: Stochastic stability 62E25
Secondary: 60B10: Convergence of probability measures 60J27: Continuous-time Markov processes on discrete state spaces 62G07: Density estimation 62G09: Resampling methods 62L10: Sequential analysis

Hidden Markov model nonlinear filter particle filter stability Hilbert metric total variation norm mixing regularizing kernel


Le Gland, François; Oudjane, Nadia. Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters. Ann. Appl. Probab. 14 (2004), no. 1, 144--187. doi:10.1214/aoap/1075828050.

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