In this paper, the forgetting of the initial distribution for a nonergodic Hidden Markov Models (HMM) is studied. A new set of conditions is proposed to establish the forgetting property of the filter. Both a pathwise and mean convergence of the total variation distance of the filter started from two different initial distributions are obtained. The results are illustrated using a generic nonergodic state-space model for which both pathwise and mean exponential stability is established.
Publié le : 2010-10-15
Classification:
Nonlinear filtering,
forgetting of the initial distribution,
nonergodic Hidden Markov Chains,
Feynman–Kac semigroup,
93E11,
60G35,
62C10
@article{1282747396,
author = {Douc, Randal and Gassiat, Elisabeth and Landelle, Benoit and Moulines, Eric},
title = {Forgetting of the initial distribution for nonergodic Hidden Markov Chains},
journal = {Ann. Appl. Probab.},
volume = {20},
number = {1},
year = {2010},
pages = { 1638-1662},
language = {en},
url = {http://dml.mathdoc.fr/item/1282747396}
}
Douc, Randal; Gassiat, Elisabeth; Landelle, Benoit; Moulines, Eric. Forgetting of the initial distribution for nonergodic Hidden Markov Chains. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp. 1638-1662. http://gdmltest.u-ga.fr/item/1282747396/