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International Journal of Stochastic Analysis
Volume 2014 (2014), Article ID 628321, 6 pages
http://dx.doi.org/10.1155/2014/628321
Research Article

Strong Law of Large Numbers for Hidden Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degrees

College of Mathematics and Information Science, Wenzhou University, Zhejiang 325035, China

Received 29 August 2014; Accepted 24 November 2014; Published 9 December 2014

Academic Editor: Lukasz Stettner

Copyright © 2014 Huilin Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. R. Rabiner, “Tutorial on hidden Markov models and selected applications in speech recognition,” Proceedings of the IEEE, vol. 77, no. 2, pp. 257–286, 1989. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Li and R. M. Gray, Image Segmentation and Compression Using Hidden Markov Models, Kluwer Academic Publishers, 2000.
  3. R. Durbin, S. Eddy, A. Krogh, and G. Mitchison, Biological Sequence Analysis, Cambridge University Press, Cambridge, UK, 1998.
  4. T. Koski, Hidden Markov Models for Bioinformatics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
  5. M. Yuan and C. Kendziorski, “Hidden Markov models for microarray time course data in multiple biological conditions,” Journal of the American Statistical Association, vol. 101, no. 476, pp. 1323–1332, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. J. D. Hamilton, “A new approach to the economic analysis of nonstationary time series and the business cycle,” Econometrica, vol. 57, no. 2, pp. 357–384, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  7. C. A. Sims and T. Zha, “Were there regime switches in U.S. monetary policy?” The American Economic Review, vol. 96, no. 1, pp. 54–81, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. Ephraim and N. Merhav, “Hidden Markov processes,” IEEE Transactions on Information Theory, vol. 48, no. 6, pp. 1518–1569, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. L. E. Baum and T. Petrie, “Statistical inference for probabilistic functions of finite state Markov chains,” Annals of Mathematical Statistics, vol. 37, pp. 1554–1563, 1966. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. T. Petrie, “Probabilistic functions of finite state Markov chains,” Annals of Mathematical Statistics, vol. 40, pp. 97–115, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. B. G. Leroux, “Maximum-likelihood estimation for hidden Markov models,” Stochastic Processes and their Applications, vol. 40, no. 1, pp. 127–143, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. P. J. Bickel and Y. Ritov, “Inference in hidden Markov models. I. Local asymptotic normality in the stationary case,” Bernoulli, vol. 2, no. 3, pp. 199–228, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  13. I. Benjamini and Y. Peres, “Markov chains indexed by trees,” The Annals of Probability, vol. 22, no. 1, pp. 219–243, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. Huang and W. Yang, “Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree,” Science in China Series A: Mathematics, vol. 51, no. 2, pp. 195–202, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus