Stability and approximation of nonlinear filters using the Hilbert metric, and applications to particle filters
Le Gland, François ; Oudjane, Nadia
HAL, hal-00912083 / Harvested from HAL
Text on HAL
The stability of the optimal filter w.r.t. its initial condition and w.r.t. the model, is studied in a general hidden Markov model using the Hilbert projective metric. These stability results are then used to prove the uniform convergence of the interacting particle filter to the optimal filter, as the number of particles goes to infinity.
Publié le : 2000-12-05
Classification:  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00912083,
     author = {Le Gland, Fran\c cois and Oudjane, Nadia},
     title = {Stability and approximation of nonlinear filters using the Hilbert metric, and applications to particle filters},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00912083}
}

Le Gland, François; Oudjane, Nadia. Stability and approximation of nonlinear filters using the Hilbert metric, and applications to particle filters. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00912083/