## The Annals of Applied Probability

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 3 February 2004

https://projecteuclid.org/euclid.aoap/1075828050

Digital Object Identifier
doi:10.1214/aoap/1075828050

Mathematical Reviews number (MathSciNet)
MR2023019

Zentralblatt MATH identifier
1060.93094

#### Citation

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. https://projecteuclid.org/euclid.aoap/1075828050

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