Some Limit Theorems for Nonhomogeneous Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degree

Kangkang Wang

Abstract

In this paper, a generalized Shannon-McMillan theorem for the nonhomogeneous Markov chains indexed by an infinite tree which has a uniformly bounded degree is discussed by constructing a nonnegative martingale and analytical methods. As corollaries, some Shannon-Mcmillan theorems for the nonhomogeneous Markov chains indexed by a homogeneous tree and the nonhomogeneous Markov chain are obtained. Two results which have been obtained are extended.