The Annals of Applied Probability

Forgetting of the initial distribution for nonergodic Hidden Markov Chains

Randal Douc, Elisabeth Gassiat, Benoit Landelle, and Eric Moulines

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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.

Article information

Source
Ann. Appl. Probab. Volume 20, Number 5 (2010), 1638-1662.

Dates
First available in Project Euclid: 25 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1282747396

Digital Object Identifier
doi:10.1214/09-AAP632

Mathematical Reviews number (MathSciNet)
MR2724416

Zentralblatt MATH identifier
1197.93158

Subjects
Primary: 93E11: Filtering [See also 60G35] 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Nonlinear filtering forgetting of the initial distribution nonergodic Hidden Markov Chains Feynman–Kac semigroup

Citation

Douc, Randal; Gassiat, Elisabeth; Landelle, Benoit; Moulines, Eric. Forgetting of the initial distribution for nonergodic Hidden Markov Chains. Ann. Appl. Probab. 20 (2010), no. 5, 1638--1662. doi:10.1214/09-AAP632. https://projecteuclid.org/euclid.aoap/1282747396


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