关键词: Cayley tree, random field, Markov chains field, strong law of large numbers,Shannon-McMillan theorem

Abstract:

This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. conver-gence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.

Key words: Cayley tree, random field, Markov chains field, strong law of large numbers,Shannon-McMillan theorem