可列m重非齐次马氏链的遍历性与熵率  

The Ergodic and Entropy Rate of mth-order Countable Nonhomogeneous Markov Chains

作　　者：姜蕾[1] 王豹[2] 

机构地区：[1]鲁东大学数学与信息学院,烟台264025 [2]徐州工程学院,徐州221008

出　　处：《工程数学学报》2010年第3期446-454,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10571076)~~

摘　　要：本文在研究可列m重非齐次马氏链各种遍历性定义的基础上,以转移概率引入可列m重非齐次马氏链绝对平均强遍历性的概念,通过设定可列m重非齐次马氏链满足这种强遍历的充分条件,得出可列m重非齐次马氏链泛函的一个极限定理,并应用此极限定理得到了可列m重非齐次马氏链熵率存在的一个定理。On the basis of analyzing various definitions for ergodic, this paper introduces the notion of absolute mean strong ergodic of mth-order countable nonhomogeneous Markov chains by means of the transition probability. By setting a sufficient condition for the mth-order countable nonhomogeneous Markov chains, a limit theorem for the mth-order countable nonhomogeneous Markov chains functional is obtained. Furthermore, we get a theorem that the entropy rate of mth-order countable nonhomogeneous Markov chains exists by using this limit theorem.

关 键 词：非齐次马氏链 遍历性 转移矩阵 

分 类 号：O211.62[理学—概率论与数理统计]