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

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

2009-10-19

arxiv.org/abs/0910.3603v2

Annals of Applied Probability 2010, Vol. 20, No. 6, 2318-2345

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP688 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP688

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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