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2010 Asia-Pacific Conference on Information Theory (APCIT 2010 E-BOOK)

Xi'an,China,10.1-10.2,2010

ISBN: 978-1-935068-47-1 Scientific Research Publishing, USA

E-Book 506pp Pub. Date: November 2010

Category: Computer Science & Communications

Price: $80

Title: An Existence Theorem for Sample Relative Entropy Rate of Non-Homogeneous Markov Chains
Source: 2010 Asia-Pacific Conference on Information Theory (APCIT 2010 E-BOOK) (pp 370-374)
Author(s): Yue Zhang, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
Weiguo Yang, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
Abstract: Sample relative entropy rate is an important content of information theory, and it plays an impor- tant role in the statistical hypothesis testing and coding theory. The purpose of this paper is to study the exis- tence for sample relative entropy rate of non-homogenous Markov chains takes values in the finite state. Firstly, we extend the definition of mean absolute convergence for the series to the plane, and obtain the defi- nition and corresponding lemmas of the mean absolute convergence for the plane. Then using a limit theorem for the averages of the functions of two variables and the strong law of large numbers of non-homogeneous Markov chains, we give the existence conditions for sample relative entropy rate of non- homogeneous Mar- kov chains. In this paper, the hypothesis testing problem on independent and identical distributed random va- riables of information theory is extended.
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