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December 2010 A complete solution to Blackwell’s unique ergodicity problem for hidden Markov chains
Pavel Chigansky, Ramon van Handel
Ann. Appl. Probab. 20(6): 2318-2345 (December 2010). DOI: 10.1214/10-AAP688

Abstract

We develop necessary and sufficient conditions for uniqueness of the invariant measure of the filtering process associated to an ergodic hidden Markov model in a finite or countable state space. These results provide a complete solution to a problem posed by Blackwell (1957), and subsume earlier partial results due to Kaijser, Kochman and Reeds. The proofs of our main results are based on the stability theory of nonlinear filters.

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Pavel Chigansky. Ramon van Handel. "A complete solution to Blackwell’s unique ergodicity problem for hidden Markov chains." Ann. Appl. Probab. 20 (6) 2318 - 2345, December 2010. https://doi.org/10.1214/10-AAP688

Information

Published: December 2010
First available in Project Euclid: 19 October 2010

zbMATH: 1202.93159
MathSciNet: MR2759736
Digital Object Identifier: 10.1214/10-AAP688

Subjects:
Primary: 93E11
Secondary: 37A50 , 60J05 , 60J10 , 93E15

Keywords: asymptotic stability , Filtering , Hidden Markov models , unique ergodicity

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.20 • No. 6 • December 2010
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