双根树上二阶非齐次马氏链的强大数定律和Shannon-McMillan定理  

The Strong Law of Large Numbers and the ShannonMcMillan Theorem for the Two-Order Nonhomogeneous Markov Chains Indexed by an Two Rooted Cayley Tree

作　　者：石志岩[1] 韩大钊 杨卫国[1] 

机构地区：[1]江苏大学理学院

出　　处：《应用概率统计》2015年第2期125-134,共10页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(11226210;11071104);江苏大学高级人才启动基金(11JDG116);江苏省教育厅统计应用研究基地;2014年江苏大学统计学校级重点学科资助

摘　　要：本文首先研究了双根树上转移矩阵为逐点转移的二阶非齐次马氏链的强极限定理,同时得到双根树上二阶非齐次马氏链的强大数定律.最后,给出了双根树上二阶非齐次马氏链几乎处处收敛意义下的Shannon-McMillan定理.In this paper, we first study the strong convergence theorem for finite two-order nonhomogeneous Markov chains indexed by an two rooted Cayley tree, then we obtain the strong law of large numbers for this Maxkov chains. Finally, we obtain the Shannon-McMiUan theorem with a.e. convergence for an two-order nonhomogeneous Markov chain indexed by an two rooted Cayley tree.

关 键 词：双根树 二阶非齐次马氏链 强大数定律 SHANNON-MCMILLAN定理 

分 类 号：O211.6[理学—概率论与数理统计]