摘要
利用分析方法研究了马氏环境中马氏链的若干强极限定理.得到了关于此种链四元函数的一个强极限定理.作为推论,得到了马氏环境中马氏链相对熵密度的几个极限性质,将Shannon定理推广到了马氏环境中马氏链的情况.
Some strong limit theorems of Markov chains in Markovian environments are studied by analysis method. And a strong limit theorem for the functions of four variables related to these chains is obtained. As corollaries, some limit properties of relative entropy density of Markov chains in Markovian environments are gotten. Finally, the Shannon theorem to the case of Markov chains in Markovian environments is promoted.
出处
《数学进展》
CSCD
北大核心
2008年第5期539-550,共12页
Advances in Mathematics(China)
基金
国家自然科学基金(No.10771021,No.10471012)
教育部留学回国人员科研启动基金(No.[2005]564)资助项目.
关键词
马氏环境
马氏链
强极限
相对熵密度
Markovian environments
Markov chains
strong limit
relative entropy density