## Strong law of large numbers for countable Markov chains indexed by an infinite tree with uniformly bounded degree.(English)Zbl 1406.60048

Summary: We study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by an infinite tree with uniformly bounded degree, which extends the corresponding results of countable Markov chains indexed by a Cayley tree and generalizes the relative results of finite Markov chains indexed by a uniformly bounded tree.

### MSC:

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