Abstract:

Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields
(NSMC) on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields. The asymptotic equipartition properties with almost everywhere (a.e.) convergence for NSMC on Cayley trees are obtained.

Key words: Cayley tree, nonsymmetric Markov chain fields,
strong law of large numbers, asymptotic equipartition property