The Annals of Applied Probability

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

Pavel Chigansky and Ramon van Handel

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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.

Article information

Ann. Appl. Probab., Volume 20, Number 6 (2010), 2318-2345.

First available in Project Euclid: 19 October 2010

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Zentralblatt MATH identifier

Primary: 93E11: Filtering [See also 60G35]
Secondary: 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 60J05: Discrete-time Markov processes on general state spaces 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 93E15: Stochastic stability

Hidden Markov models filtering unique ergodicity asymptotic stability


Chigansky, Pavel; van Handel, Ramon. A complete solution to Blackwell’s unique ergodicity problem for hidden Markov chains. Ann. Appl. Probab. 20 (2010), no. 6, 2318--2345. doi:10.1214/10-AAP688.

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