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Forgetting of the initial condition for the filter in general state-space hidden Markov chain: a coupling approach


 
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1. Title Title of document Forgetting of the initial condition for the filter in general state-space hidden Markov chain: a coupling approach
 
2. Creator Author's name, affiliation, country Randal Douc; Institut Telecom/ Telecom SudParis
 
2. Creator Author's name, affiliation, country Eric Moulines; Institut Telecom/ Telecom ParisTech
 
2. Creator Author's name, affiliation, country Yaacov Ritov; Hebrew University Jerusalem
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) hidden Markov chain; stability; non-linear filtering, coupling
 
3. Subject Subject classification 93E11; 60J57
 
4. Description Abstract We give simple conditions that ensure exponential forgetting of the initial conditions of the filter for general state-space hidden Markov chain. The proofs are based on the coupling argument applied to the posterior Markov kernels. These results are useful both for filtering hidden Markov models using approximation methods (e.g., particle filters) and for proving asymptotic properties of estimators. The results are general enough to cover models like the Gaussian state space model, without using the special structure that permits the application of the Kalman filter.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Research Agency (ANR) under the program ``ANR-05-BLAN-0299
 
7. Date (YYYY-MM-DD) 2009-01-14
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/593
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-593
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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