关于m阶非齐次马氏信源的一类Shannon-McMillan定理  

A Class of Shannon-Mcmillan Theorems for m-th Order Nonhomogeneous Markov Information Source

作　　者：叶慧[1] 王康康[1,2] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003 [2]南京航空航天大学航空宇航学院,江苏南京210016

出　　处：《数学的实践与认识》2010年第20期186-192,共7页Mathematics in Practice and Theory

基　　金：江苏省高校自然科学基础研究项目(09KJD110002)

摘　　要：采用构造相容分布与非负上鞅的方法的研究m阶马氏信源广义相对熵密度的强极限定理,即广义Shannon-McMillan定理.并由此得出若干马氏信源,无记忆信源的随机Shannon-Mcmillan定理.In this paper,a class of strong limit theorems for the generalized relative entropy densities of m-th order nonhomogeneous Markov information source are discussed by constructing the joint distribution and nonnegative super martingales.As corollaries,some Shannon-Mcmillan theorems for Markov information source and non-memory information source are obtained and some results for the discrete information source which have been obtained by author are extended.

关 键 词：SHANNON-MCMILLAN定理 相容分布 m阶马氏信源 无记忆信源 相对熵密度 

分 类 号：O211.4[理学—概率论与数理统计]