An Entropy Rate Theorem for a Hidden Inhomogeneous Markov Chain
Yao Qi-feng1, Dong Yun2, Wang Zhong-Zhi1, *
Identifiers and Pagination:Year: 2017
First Page: 19
Last Page: 26
Publisher Id: TOSPJ-8-19
Article History:Received Date: 02/02/2017
Revision Received Date: 03/07/2017
Acceptance Date: 16/08/2017
Electronic publication date: 30/09/2017
Collection year: 2017
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The main object of our study is to extend some entropy rate theorems to a Hidden Inhomogeneous Markov Chain (HIMC) and establish an entropy rate theorem under some mild conditions.
A hidden inhomogeneous Markov chain contains two different stochastic processes; one is an inhomogeneous Markov chain whose states are hidden and the other is a stochastic process whose states are observable.
Materials and Methods:
The proof of theorem requires some ergodic properties of an inhomogeneous Markov chain, and the flexible application of the properties of norm and the bounded conditions of series are also indispensable.
This paper presents an entropy rate theorem for an HIMC under some mild conditions and two corollaries for a hidden Markov chain and an inhomogeneous Markov chain.
Under some mild conditions, the entropy rates of an inhomogeneous Markov chains, a hidden Markov chain and an HIMC are similar and easy to calculate.