二重非齐次马氏链的遍历性及其应用  

The Ergodic and its Applications for 2 Order Nonhomogeneous Markov Chains

作　　者：方舒[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《数学研究》2010年第1期55-66,共12页Journal of Mathematical Study

基　　金：安徽省教育厅自然科学基金(2003kjl65);安徽省高等学校青年教师科研资助基金项目(2005jql044)

摘　　要：给出二重非齐次马氏链的强遍历性,绝对平均强遍历性,Cesaro平均收敛的概念.利用二维马氏链的遍历性和C-K方程,建立了二维马氏链与二重非齐次马氏链遍历性的关系.并讨论了齐次二重马氏链绝对平均强遍历与强遍历的等价性.最后给出Cesaro平均收敛在马氏决策过程和信息论中应用.The notions of strong ergodic, the absolute average strong ergodic and Cesaro average convergence for 2 order nonhomogeneous Markov chains are defined.Based on the strong ergodie and establishing C-K equation, we discuss the relation of of the two dimensionality Markov chains and 2 order Markov chains. And we give the equivalence between the absolute average strong ergodic and strong ergodic for 2 order homogeneous Markov chains. Finally, we give some applications of this notion on Markov decision processes and information theory.

关 键 词：二重马氏链 强遍历性 绝对平均强遍历性 Cesaro平均收敛 熵率 

分 类 号：O211.62[理学—概率论与数理统计]