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Strong law of large numbers for Markov chains field on a Bethe tree. (English) Zbl 0981.60064
Summary: We study the strong law of large numbers on the frequencies of states for a Markov chain field on a Bethe tree. In the proof, we apply a new technique in the study of strong limit theorems.

60J10Markov chains (discrete-time Markov processes on discrete state spaces)
60F15Strong limit theorems
Full Text: DOI
[1] Benjamini, I.; Peres, Y.: Markov chains indexed by trees. Ann. probab. 22, 219-243 (1994) · Zbl 0793.60080
[2] Berger, T.; Ye, Z.: Entropic aspects of random fields on trees. IEEE trans. Inform. theory 36, No. 5, 1006-1018 (1990) · Zbl 0738.60100
[3] Liu, W.; Yang, W. G.: A limit theorem for the entropy density of nonhomogeneous Markov information source. Statist. probab. Lett. 22, 295-301 (1995) · Zbl 0833.60034
[4] Liu, W.; Yang, W. G.: An extension of Shannon--mcmillan theorem and some limit properties for nonhomogeneous Markov chains. Stochastic. process. 61, 129-146 (1996) · Zbl 0861.60042
[5] Spitzer, F.: Markov random fields on an infinite tree. Ann. probab. 3, 387-398 (1975) · Zbl 0313.60072
[6] Ye, Z.; Berger, T.: Ergodic regularity and asymptotic equipartition property of random fields on trees. J. combin. Inform. system sci. 21, No. 2, 157-184 (1996) · Zbl 0953.94008