The Markov approximation of the random fields on Cayley trees and a class of small deviation theorems

Statistics and Probability Letters

Volumn 63, Issue 2, 2003, Pages 113-121

  Liu, Wen ^a   Wang, Liying ^b  

^a HEBEI UNIVERSITY OF TECHNOLOGY   (China)

^b SHIJIAZHUANG TIEDAO UNIVERSITY   (China)

Author keywords

Markov chain fields on Cayley trees; Sample relative entropy rate; Small deviation theorem; Strong deviation theorem; Strong limit theorem

Indexed keywords

EID: 0037678797     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(03)00058-0     Document Type: Article

References (7)

1. Benjamini I. Peres Y. Markov chains indexed by trees Ann. Probab. 22 1994 219-243
2. Berger T. Ye Z. Entropic aspects of random fields on trees IEEE Trans. Inform. Theory 36 5 1990 1006-1018
3. Liu W. Yang W. An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains Stochastic Process. Appl. 61 1996 129-146
4. Liu W. Yang W. The Markov approximation of the sequences of N-valued random variables and a class of small deviation theorems Stochastic Process. Appl. 89 2000 117-130
5. Spitzer F. Markov random fields on an infinite tree Ann. Probab. 3 1975 387-398
6. Ye Z. Berger T. Ergodicity, regularity and asymptotic equipartition property for random fields on trees J. Combin. Inform. Syst. Sci. 21 2 1996 157-184
7. Ye Z. Berger T. Information Measure for Discrete Random Fields 1998 Science Press Beijing, New York