A class of small deviation theorems for the random fields on an m rooted Cayley tree

Abstract

In this paper, we are to establish a class of strong deviation theorems for the random fields relative to mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree. As corollaries, we obtain the strong law of large numbers and Shannon-McMillan theorem for mth-order nonhomogeneous Markov chains indexed by that tree.