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

^*Corresponding author for this work

Department of Statistics

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
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

Keywords

Asymptotic stability
Filtering
Hidden Markov models
Unique ergodicity

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10.1214/10-AAP688

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

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Keywords

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