A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains
Probability
2010-11-16 v2 Information Theory
math.IT
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.
Keywords
Cite
@article{arxiv.0910.3603,
title = {A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains},
author = {Pavel Chigansky and Ramon van Handel},
journal= {arXiv preprint arXiv:0910.3603},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AAP688 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)