Analyticity of entropy rate of hidden Markov chains

作者：Han Guangyue^*; Marcus Brian

来源：IEEE Transactions on Information Theory, 2006, 52(12): 5251-5266.

DOI：10.1109/TIT.2006.885481

• analyticity
• entropy
• entropy rate
• hidden Markov chain
• hidden Markov process

We prove that under mild positivity assumptions the, entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions, the hidden Markov chain itself varies analytically, in a strong sense, as a function of the underlying Markov chain parameters.

• 出版日期2006-12