Some Strong Limit Theorems for Even-Odd Markov Chain Fields on Binary Trees and an Approximation of Shannon-McMillan Theorem

In this paper some strong limit theorems on the frequences of states and ordered state couples for the even-odd Markov chains fields on binary trees, including the estimates of the upper bound and lower bound of asymptotic entropy density and an approximation of Shannon-McMillan theorem, are obtained. In the proof an analytic technique for the study of strong limit theorems of Markov chains is extened to the case of Markov chain fields.