A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains

Pavel Chigansky; Ramon Van Handel

doi:10.1214/10-AAP688

A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains

Pavel Chigansky, Ramon Van Handel

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2318-2345
Number of pages	28
Journal	Annals of Applied Probability
Volume	20
Issue number	6
DOIs	https://doi.org/10.1214/10-AAP688
State	Published - Dec 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Asymptotic stability
Filtering
Hidden Markov models
Unique ergodicity

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10.1214/10-AAP688

Cite this

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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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AU - Van Handel, Ramon

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AB - 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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KW - Unique ergodicity

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A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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