二叉树分枝马氏链的强大数定律和Shannon-McMillan定理  

The Strong Law of Large Numbers and the Shannon-McMillan Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree

作　　者：张艳[1] 杨卫国[1] 

机构地区：[1]江苏大学理学院,镇江212013

出　　处：《应用概率统计》2017年第4期408-416,共9页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11571142)资助

摘　　要：首先研究二叉树有限状态分枝马氏链的随机序偶出现频率的强大数定律,之后研究二叉树有限状态分枝马氏链函数的强大数定律,作为推论得到二叉树有限状态分枝马氏链的ShannonMcMillan定理.In this paper, we first study the strong law of large numbers for the frequencies of occurrenceof random ordered couples of states for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Then the strong law of large numbers are studied for functions of the nonhomogeneous bifurcating Markov chains indexed by a binary tree. As a corollary, we obtain the shannon-McMillan theorem for these Markov chains with finite state space.

关 键 词：二叉树 非齐次马氏链 强大数定律 SHANNON-MCMILLAN定理 

分 类 号：O211.4[理学—概率论与数理统计] O211.6[理学—数学]