The Approximation to the Random Fields Indexed by a Non-homogeneous Tree

The strong deviation theorem is one of the central questions for studying in the international probability theory. This paper brings in relative entropy ratio of sample as a measure of deviation between arbitrary random field and Markov random fields of order two on a non-homogeneous tree, and gives a strong deviation theorem on arbitrary probability measure of (Omega, F) by constructing a martingale and using Doob´s martingale convergence theorem.