Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters
Le Gland, François ; Oudjane, Nadia
Ann. Appl. Probab., Tome 14 (2004) no. 1, p. 144-187 / Harvested from Project Euclid
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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.
Publié le : 2004-02-14
Classification:  Hidden Markov model,  nonlinear filter,  particle filter,  stability,  Hilbert metric,  total variation norm,  mixing,  regularizing kernel,  93E11,  93E15,  62E25,  60B10,  60J27,  62G07,  62G09,  62L10 
@article{1075828050,
     author = {Le Gland, Fran\c cois and Oudjane, Nadia},
     title = {Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters},
     journal = {Ann. Appl. Probab.},
     volume = {14},
     number = {1},
     year = {2004},
     pages = { 144-187},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1075828050}
}

Le Gland, François; Oudjane, Nadia. Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp.  144-187. http://gdmltest.u-ga.fr/item/1075828050/