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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 502808, 8 pages
http://dx.doi.org/10.1155/2014/502808
Research Article

A New Multivariate Markov Chain Model for Adding a New Categorical Data Sequence

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

Received 10 July 2013; Revised 26 January 2014; Accepted 10 February 2014; Published 23 March 2014

Academic Editor: Andrzej Swierniak

Copyright © 2014 Chao Wang et al. 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. H. S. Wang and N. Moayeri, “Finite-state Markov channel—a useful model for radio communication channels,” IEEE Transactions on Vehicular Technology, vol. 44, no. 1, pp. 163–171, 1995. View at Publisher · View at Google Scholar · View at Scopus
  2. F. P. Kelly, “Stochastic models of computer communication systems,” Journal of the Royal Statistical Society B, vol. 47, no. 3, pp. 379–395, 1985. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. E. van der Laan and M. Salomon, “Production planning and inventory control with remanufacturing and disposal,” European Journal of Operational Research, vol. 102, no. 2, pp. 264–278, 1997. View at Google Scholar · View at Scopus
  4. M. Gales and S. Young, “The application of hidden Markov models in speech recognition,” Foundations and Trends in Signal Processing, vol. 1, no. 3, pp. 195–304, 2008. View at Google Scholar
  5. C. P. C. Lee, G. H. Golub, and S. A. Zenios, “A fast two-stage algorithm for computing PageRank and its extensions,” Tech. Rep. SCCM-200315, Scientific Computation and Computational Mathematics, Stanford University, 2003. View at Google Scholar
  6. S. Kamvar, T. Haveliwala, and G. Golub, “Adaptive methods for the computation of PageRank,” Linear Algebra and Its Applications, vol. 386, pp. 51–65, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. N. Langville and C. D. Meyer, Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, 2006.
  8. S. L. Salzberg, A. L. Deicher, and S. Kasif, “Microbial gene identification using interpolated Markov models,” Nucleic Acids Research, vol. 26, no. 2, pp. 544–548, 1998. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Frydman, “A nonparametric estimation procedure for a periodically observed three-state Markov process, with application to AIDS,” Journal of the Royal Statistical Society B, vol. 54, no. 3, pp. 853–866, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W.-K. Ching, E. S. Fung, and M. K. Ng, “A multivariate Markov chain model for categorical data sequences and its applications in demand predictions,” IMA Journal of Management Mathematics, vol. 13, no. 3, pp. 187–199, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. W. Ching, M. M. Ng, and E. S. Fung, “On construction of stochastic genetic networks based on gene expression sequences,” International Journal of Neural Systems, vol. 15, no. 4, pp. 297–310, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. G. D'Amico, J. Janssen, and R. Manca, “Initial and final backward and forward discrete time non-homogeneous semi-markov credit risk models,” Methodology and Computing in Applied Probability, vol. 12, no. 2, pp. 215–225, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. Psaradakis, M. Sola, and F. Spagnolo, “On markov error-correction models, with an application to stock prices and dividends,” Journal of Applied Econometrics, vol. 19, no. 1, pp. 69–88, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. W. Ching, T. Siu, and L. Li, “An improved parsimonious multivariate Markov chain model for credit risk,” Journal of Credit Risk, vol. 5, pp. 1–25, 2009. View at Google Scholar
  15. N. J. Jobst and S. A. Zenios, “Extending credit risk (pricing) models for the simulation of portfolios of interest rate and credit risk sensitive securities,” Wharton School Centre for Financial Institutions Working Papers 01-25, 2001. View at Google Scholar
  16. B.-Y. Pu, T.-Z. Huang, and C. Wen, “A new GMRES(m) method for Markov chains,” Mathematical Problems in Engineering, vol. 2013, Article ID 206375, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. L. C. Lin and S. Yau, “Analyzing Taiwan IC assembly industry by Grey-Markov forecasting model,” Wu Mathematical Problems in Engineering, vol. 2013, Article ID 658630, 6 pages, 2013. View at Publisher · View at Google Scholar
  18. M. Davis and V. Lo, “Modeling default correlation in bond portfolios,” in Mastering Risk, vol. 2, pp. 141–151, Financial Times Management, 2001. View at Google Scholar
  19. M. Kijima, K. Komoribayashi, and E. Suzuki, “A multivariate Markov model for simulating correlated defaults,” Journal of Risk, vol. 4, pp. 1–32, 2002. View at Google Scholar
  20. A. E. Raftery, “A model for high-order Markov chains,” Journal of the Royal Statistical Society B, vol. 47, no. 3, pp. 528–539, 1985. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. T.-K. Siu, W.-K. Ching, and E. S. Fung, “On a multivariate Markov chain model for credit risk measurement,” Quantitative Finance, vol. 5, no. 6, pp. 543–556, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. D.-M. Zhu and W.-K. Ching, “A note on the stationary property of high-dimensional Markov chain models,” International Journal of Pure and Applied Mathematics, vol. 66, no. 3, pp. 321–330, 2011. View at Google Scholar · View at MathSciNet
  23. C. T. Haan, D. M. Allen, and J. O. Street, “A Markov chain model of daily rainfall,” Water Resources Research, vol. 12, no. 3, pp. 443–449, 1976. View at Google Scholar · View at Scopus
  24. E. Seneta, Non-negative Matrices and Markov Chain, Springer, New York, NY, USA, 1981. View at MathSciNet