非齐次树上m重非齐次马氏信源的Shannon-McMillan定理

摘要

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.本文利用相对熵密度和随机条件熵的概念,通过构造适当的辅助非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究给出了非齐次树上m重非齐次马氏信源的一类Shannon-McMillan定理.%In recent years,tree indexed stochastic process has become one of the research directions in the probability theory.The strong limit theorem has been one of the central issues of the international probability theory.In this paper,by applying the concept of the relative entropy density and the random condition entropy,and through constructing an appropriate non-negative martingale,Shannon-McMillan theorem of m ordered non-homogeneous Markov information source on a non-homogeneous tree is given.