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Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree. (English) Zbl 1141.60011
Summary: In this paper, we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree. The results generalize the analogous results on a homogeneous tree.

##### MSC:
 60F15 Strong limit theorems 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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##### References:
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