任意齐次树指标马氏链场的一类Shannon-Mcmillan定理

A Class of Shannon-Mcmillan Theorems for Markov Chains Field Indexed by a Homogeneous Tree

采用构造相容分布与非负上鞅的方法来研究任意齐次树指标可列非齐次马氏链场的相对熵密度的一类强极限定理,并由此得出若干齐次树指标有限状态非齐次马氏链场、一般非齐次马氏链的Shannon-Mcmillan定理.将已有的关于离散信源的结果加以推广.

In this paper, a class of strong limit theorems for the relative entropy densi- ties of Markov chains field indexed by a homogeneous tree are discussed by constructing the joint distribution and nonnegative super martingales. As corollaries, some Shannon-Mcmillan theorems for the finite Markov chains field indexed by a homogeneous tree, the general non- homogeneous Markov chain are obtained and some results for the discrete information source which have been obtained by author are extended.