Forgetting of the initial distribution for nonergodic Hidden Markov Chains
Randal Douc, Elisabeth Gassiat, Benoit Landelle, and Eric Moulines
Source: Ann. Appl. Probab. Volume 20, Number 5
(2010), 1638-1662.
Abstract
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.
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Keywords: Nonlinear filtering; forgetting of the initial distribution; nonergodic Hidden Markov Chains; Feynman–Kac semigroup
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1282747396
Digital Object Identifier: doi:10.1214/09-AAP632
Zentralblatt MATH identifier: 05795066
Mathematical Reviews number (MathSciNet): MR2724416
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