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Some Strong Limit Theorems Relative to the Geometric Average of Random Transition Probabilities of Nonhomogenemous Markov Chains Indexed by a Tree

In this paper, we study some strong limit theorems relative to the geometric average of random transition probabilities of nonhomogeneous Markov chains indexed by a tree. This result is an extension of some strong limit theorems relative to the geometric average of random transition probabilities of arbitrary finite nonhomogeneous Markov chains.