摘要
本文引进有限非齐次马氏链随机条件熵的概念,研究了这个概念和相对熵密度的关系,并利用数列绝对平均收敛的概念给出了有限非齐次马氏链{X_n}的相对熵密度及其平均随机条件熵 a.e.收敛于常数以及{X_n}的熵率存在的条件,推广了Shannon 的一个定理.
In this paper,the notion of random conditional entropy of finite non-homog- eneous Markov chains is introduced,and the relation between this notion and the relative entropy density is studied.By using the notion of the absolute mean convergence of sequences,the conditions of relative entropy density and the mean random conditional entropy of finite non-homogeneous Markov chains {X_n}being convergent to a constant a.e.and the existence of entr- opy rate of {X_n} are given.The results are the extensions of a theorem of Shannon.
出处
《河北工学院学报》
1990年第4期65-78,共14页
Journal of Hubei Polytechnic University
关键词
相对熵密度
随机条件熵
马氏链
Relative entropy density
Random conditional entropy
Markov chains
Convergence almost everywhere
