References
- Algoet, P.H., Cover, T.M. (1988). A sandwich proof of the Shannon- Mcmillan-Breiman theorem. Ann. Probab. 16(2):899–909.
- Barron, A.R. (1985). The strong ergodic theorem for densities: Generalized Shannon-Mcmillan–Breiman theorem. Ann. Probab. 13:1292–1303.
- Benjamini, I., Peres, Y. (1994). Markov chains indexed by trees. Ann. Probab. 22:219–243.
- Berger, T., Ye, Z. (1990). Entropic aspects of random fields on trees. IEEE Trans. Inform. Theory 36:1006–1018.
- Breiman, L. (1957). The individual ergodic theorem of information theory. Ann. Math. Stat. 28:809–811. With correction made in 31:809-810.
- Chung, K.L. (1961). The ergodic theorem of information theory. Ann. Math. Stat. 32:612–614.
- Huang, H.L., Yang, W.G. (2008). Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree. Sci. Chin. Ser. A: Math. 51(2):195–202.
- Liu, W., Yang, W.G. (1996). A extension of Shannon-Mcmillan theorem and some limit properties for nonhomogeneous Markov chains. Stochastic Process. Appl. 61:129–145.
- McMillan, B. (1953). The basic theorems of information theory. Ann. Math. Stat. 24:196–219.
- Pemantle, R. (1992). Andomorphism invariant measure on tree. Ann. Probab. 20:1549–1566.
- Shannon, C.E. (1948). A mathematical theory of communication. Bell Syst. Tech. J. 27:379–423, 623–656.
- Shi, Z.Y., Yang, W.G. (2009). Some limit properties of random transition probability for seconed-order nonhomogeneous Markov chains indexed by a tree. J. Inequalities Appl. ID 503203.
- Shi, Z.Y., Yang, W.G. (2010). Some limit properties for the Mth-order nonhomogeneous Markov chains indexed by a M rooted Cayley tree. Stat. Probab. Lett. 80:1223–1233.
- Yang, W.G. (2003). Some limit properties for Markov chains indexed by a homogeneous tree. Stat. Prob. Lett. 65:241–250.
- Yang, W.G., Liu, W. (2000). Strong law of large numbers for Markov chains fields on a bethe tree. Stat. Probab. Lett. 49:245–250.
- Yang, W.G., Liu, W. (2004). The asymptotic equipartition property for Mth-order nonhomogeneous Markov information sources. IEEE Trans. Inform. Theory 50(12):3326–3330.
- Yang, W.G., Yang, Z., Pan, H. (2013). Strong laws of large numbers for asymptotic even–odd Markov chains indexed by a homogeneous tree. J. Math. Anal. Appl. http://dx.doi.org/10.1016/j.jmaa.2013.08.009.
- Yang, W.G., Ye, Z. (2007). The asymptotic equipartition property for Markov chains indexed by a homogeneous tree. IEEE Trans. Inform. Theory 53(9):3275–3280.
- Ye, Z., Berger, T. (1996). Ergodic, regularity and asymptotic equipartition property of random fields on trees. Combin. Inform. Syst. Sci. 21:157–184.
- Ye, Z., Berger, T. (1998). Information Measure for Discrete Random Field. Beijing: Science.