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Journal Articles The Annals of Applied Probability Year : 2004

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

Nadia Oudjane
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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.

Dates and versions

hal-00912081 , version 1 (01-12-2013)

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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, 2004, 14 (1), pp.144-187. ⟨10.1214/aoap/1075828050⟩. ⟨hal-00912081⟩
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