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A class of small deviation theorems for the random fields on an \(m\) rooted Cayley tree. (English) Zbl 1274.60101

Summary: In this paper, we are to establish a class of strong deviation theorems for the random fields relative to \(m\)th-order nonhomogeneous Markov chains indexed by an \(m\) rooted Cayley tree. As corollaries, we obtain the strong law of large numbers and Shannon-McMillan theorem for \(m\)th-order nonhomogeneous Markov chains indexed by that 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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