An Existence Theorem for Sample Relative Entropy Rate of Non-Homogeneous Markov Chains
Yue Zhang · Gongcheng shuxue xuebao · 2012
Sample relative entropy rate is an important content of information theory,and plays an important role in statistical hypothesis testing and coding theory.The purpose of this paper is to study the existence for sample relative entropy rate of non-homogenous Markov chains that take values in the finite state.Firstly,we extend the definition of absolute mean convergence for the series to the plane,and achieve the definition and corresponding lemmas of the absolute mean convergence for the series on the plane.Then by using a limit theorem for the averages of the functions of two variables and the strong large-mumber law of non-homogeneous Markov chains,we give the existence conditions for sample relative entropy rate of non-homogeneous Markov chains.This paper entends the hypothesis testing problem on independent and identical distributed random variables in information theory to a wider range of areas.