Abstract
In this paper, we are going to study the strong law of large numbers and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in random environment. Firstly, we give the definition of Markov chains indexed by an infinite tree with uniformly bounded degree in random environment. Then, we establish some strong limit theorems that are the basis of the main result. Finally, we prove the strong law of large numbers and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in Markovian environment.
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