## Analyticity of Entropy Rate of Hidden Markov Chains With Continuous Alphabet

- Guangyue Han, Brian H. Marcus
- IEEE Transactions on Information Theory
- 2015

3 Excerpts

- Published 2010 in 2010 IEEE International Symposium on Information…

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.

@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}
}