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On Convergence of the Entropy Rate of Binary Hidden Markov Processes
Shuangping Chen *
Department of Computer Science, Zhuhai Campus, Jinan University
*Correspondence author
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Funding: 国家自然科学基金,暨南大学青年基金（No.60802026,51208030）
Opened online: 5 January 2010
Accepted by: none
Citation: Shuangping Chen.On Convergence of the Entropy Rate of Binary Hidden Markov Processes[OL]. [ 5 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38466
 
 
How fast does the entropy rate of a hidden Markov process converge to its theoretical value? Empirically, several examples have shown that the convergence is exponential, but there does not have a theoretical proof. In this paper, a special kind of binary hidden Markov processes (BHMPs) is shown to be related to cookie-cutter sets. As a result, the entropy rate of these BHMPs could be studied based on the theoretical results of cookie-cutter sets. It is proved that the estimated bias of entropy rate of such BHMPs decreases at least exponentially to zero. These conclusions are important in both theoretical and practical terms.
Keywords:Binary hidden Markov process;convergence of entropy rate;cookie-cutter set
 
 
 

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