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

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.