Entropy rate of continuous-state hidden Markov chains

Abstract

We prove that under mild positivity assumptions, the entropy rate of a continuous-state hidden Markov chain, observed when passing a finite-state Markov chain through a discrete-time continuous-output channel, is analytic as a function of the transition probabilities of the underlying Markov chain. We further prove that the entropy rate of a continuous-state hidden Markov chain, observed when passing a mixing finite-type constrained Markov chain through a discrete-time Gaussian channel, is smooth as a function of the transition probabilities of the underlying Markov chain.

DOI: 10.1109/ISIT.2010.5513590

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Cite this paper

@article{Han2010EntropyRO, title={Entropy rate of continuous-state hidden Markov chains}, author={Guangyue Han and Brian H. Marcus}, journal={2010 IEEE International Symposium on Information Theory}, year={2010}, pages={1468-1472} }