Some strong limit theorems for Markov chain fields on trees

Probability in the Engineering and Informational Sciences

Volumn 18, Issue 3, 2004, Pages 411-422

  Liu, Wen ^a   Yang, Weiguo ^b  

^a HEBEI UNIVERSITY OF TECHNOLOGY   (China)

^b JIANGSU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

FORESTRY; GRAPH DATABASES;

CAYLEY TREES; LIMIT THEOREM; PROBABILITY THEORY; SHANNON;

MARKOV CHAINS;

EID: 5644271941     PISSN: 02699648     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0269964804183083     Document Type: Article

References (7)

1. Benjamini, I. & Peres, Y. (1994). Markov chains indexed by trees. Annals of Probability 22: 219-243.
2. Berger, T. & Ye, Z. (1990). Entropic aspects of random fields on trees. IEEE Transactions on Information Theory 36(5): 1006-1018.
3. Feller, W. (1968). An introduction to probability theory and its applications, Vol. 1, 3rd ed. New York: Wiley.
4. Liu, W. & Yang, W. G. (1995). A limit theorem for the entropy density of nonhomogeneous Markov information source. Statistics and Probability Letters 22: 295-301.
5. Liu, W. & Yang, W. G. (1996). An extension of Shannon-McMillan theorem and some limit properties for nonhomogeneous Markov chains. Stochastic Processes and Their Applications 61: 129-146.
6. Spitzer, F. (1975). Markov random fields on an infinite tree. Annals of Probability 3: 387-398.
7. Ye, Z. & Berger, T. (1996). Ergodic, regularity and asymptotic equipartition property of random fields on trees. Journal of Combinatorics, Information and System Sciences 21(2): 157-184.