Analyticity of Entropy Rates of Continuous-State Hidden Markov Models
Information Theory
2019-09-02 v3 math.IT
Statistics Theory
Statistics Theory
Abstract
The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates is shown for analytically parameterized models. The obtained results hold under relatively mild conditions and cover several classes of hidden Markov models met in practice. These results are relevant for several (theoretically and practically) important problems arising in statistical inference, system identification and information theory.
Keywords
Cite
@article{arxiv.1806.09589,
title = {Analyticity of Entropy Rates of Continuous-State Hidden Markov Models},
author = {Vladislav Z. B. Tadic and Arnaud Doucet},
journal= {arXiv preprint arXiv:1806.09589},
year = {2019}
}