Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 52, 2023 - Issue 8
Submit an article Journal homepage
60
Views
2
CrossRef citations to date
0
Altmetric
Articles

Shannon-McMillan theorem and strong law of large numbers for Markov chains indexed by generalized spherically symmetric trees

Weicai Penga Department of Mathematics and Statistic, Chaohu University, Anhui, ChinaCorrespondence[email protected]
View further author information
&
Xinyue Xib School of Mathematical Science, Jiangsu University, Jiangsu, ChinaView further author information
Pages 2562-2573 | Received 23 Feb 2021, Accepted 09 Jul 2021, Published online: 25 Jul 2021

References

  • Benjamini, I., and Y. Peres. 1994. Markov chains indexed by trees. The Annals of Probability 22 (1):219–43. doi:10.1214/aop/1176988857.
  • Berger, T., and Z. Ye. 1990. Entropic aspects of random fields on trees. IEEE Transactions on Information Theory 36 (5):1006–18. doi:10.1109/18.57200.
  • Ding, C., Z. Shi, and W. Yang. 2021. The strong law of large numbers and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in random environment. Communications in Statistics-Theory and Methods 50 (15):3573–85. doi:10.1080/03610926.2019.1708398.
  • Huang, H., and W. Yang. 2008. Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree. Science in China Series A: Mathematics 51 (2):195–202. doi:10.1007/s11425-008-0015-1.
  • Peng, W. 2017. Conditional entropy, entropy density, and strong law of large numbers for generalized controlled tree-indexed Markov chains. Communications in Statistics - Theory and Methods 46 (23):11880–91. doi:10.1080/03610926.2017.1285935.
  • Peng, W., W. Yang, and Z. Shi. 2015. Strong law of large numbers for Markov chains indexed by spherically symmetric trees. Probability in the Engineering and Informational Sciences 29 (3):473–81. doi:10.1017/S0269964815000108.
  • Shi, Z., H. Zhou, and Y. Fan. 2020. A class of small deviation theorems for functionals of random fields on double Cayley tree in random environment. Stochastics 92 (8):1139–56. doi:10.1080/17442508.2019.1691209.
  • Takacs, C. 2002. Strong law of large numbers for branching Markov chains. Markov Process Related Fields 8 (1):107–16.
  • Wang, K., and D. Zong. 2011. Some Shannon-McMillan approximation theorems for Markov chain field on the generalized Bethe tree. Journal of Inequalities and Applications 2011 (1):470910. doi:10.1155/2011/470910.
  • Yang, W. 2003. Some limit properties for Markov chains indexed by a homogeneous tree. Statistics & Probability Letters 65 (3):241–50. doi:10.1016/j.spl.2003.04.001.
  • Yang, W., and W. Liu. 2001. Strong law of large numbers and Shannon-McMillan theorem for Markov chains field on Cayle tree. Acta Mathematica Scientia 21 (4):495–502. doi:10.1016/S0252-9602(17)30438-1.
  • Yang, W., and Z. Ye. 2007. Asympotoic equipartition property for nonhomogeneous Markov chains indexed by a homogeneous tree. IEEE Transactions on Information Theory 53 (9):3275–80. doi:10.1109/TIT.2007.903134.
  • Ye, Z., and T. Berger. 1996. Ergodic, regularly and asymptotic equipartition property of random fields on trees. Journal of Combinatorics, Information and System Sciences 21 :157–84.
  • Zhong, P., Z. Shi, W. Yang, and F. Min. 2021. A class of strong deviation theorems for the random fields associated with bifurcating Markov chains indexed by a binary tree. Communications in Statistics - Theory and Methods 50 (5):1210–27. doi:10.1080/03610926.2019.1648830.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.