非齐次马氏链样本相对熵率存在定理

样本相对熵率是信息论中一个重要的内容,在统计假设检验及编码理论中起着非常重要的作用.本文的目的是要研究在有限状态空间中取值的非齐次马氏链样本相对熵率的存在性.首先将数列绝对平均收敛的定义推广到平面上,并得到平面点列绝对平均收敛的定义及相关引理,然后利用非齐次马氏链二元函数的一类平均极限定理及强大数定律,给出非齐次马氏链样本相对熵率存在的条件.本文将信息论中关于独立同分布随机变量序列的假设检验问题做了更为广泛的推广.

An Existence Theorem for Sample Relative Entropy Rate of Non-Homogeneous Markov Chains

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.