A Strong Law of Large Numbers for Markov Chain Fields on a Special Non-homogeneous Tree

摘要

The strong laws of large numbers is one of the central questions for studying in the international Probability theory. In this paper, a strong law of large numbers for Markov chain fields on a special non-homogeneous tree is given by constructing a non-negative martingale and using Doobpsilas martingale convergence theorem.