Table of Contents
International Journal of Stochastic Analysis
Volume 2013, Article ID 842981, 7 pages
Research Article

A Stochastic Diffusion Process for the Dirichlet Distribution

Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Received 19 December 2012; Accepted 1 March 2013

Academic Editor: Hong K. Xu

Copyright © 2013 J. Bakosi and J. R. Ristorcelli. 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. N. L. Johnson, “An approximation to the multinomial distribution some properties and applications,” Biometrika, vol. 47, no. 1-2, pp. 93–102, 1960. View at Google Scholar
  2. J. E. Mosimann, “On the compound multinomial distribution, the multivariate-distribution, and correlations among proportions,” Biometrika, vol. 49, no. 1-2, pp. 65–82, 1962. View at Google Scholar
  3. S. Kotz, N. L. Johnson, and N. Balakrishnan, Continuous Multivariate Distributions: Models and Applications, Wiley Series in Probability and Statistics: Applied Probability and Statistics, Wiley, 2000.
  4. K. Pearson, “Mathematical contributions to the theory of evolution. On a form of spurious correlation which may arise when indices are used in the measurement of organs,” Royal Society of London Proceedings Series I, vol. 60, pp. 489–498, 1896. View at Google Scholar
  5. C. D. M. Paulino and C. A. de Bragança Pereira, “Bayesian methods for categorical data under informative general censoring,” Biometrika, vol. 82, no. 2, pp. 439–446, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. F. Chayes, “Numerical correlation and petrographic variation,” The Journal of Geology, vol. 70, pp. 440–452, 1962. View at Google Scholar
  7. P. S. Martin and J. E. Mosimann, “Geochronology of pluvial lake cochise, Southern Arizona, [part] 3, pollen statistics and pleistocene metastability,” American Journal of Science, vol. 263, no. 4, pp. 313–358, 1965. View at Publisher · View at Google Scholar
  8. K. Lange, “Applications of the Dirichlet distribution to forensic match probabilities,” Genetica, vol. 96, no. 1-2, pp. 107–117, 1995. View at Publisher · View at Google Scholar
  9. C. Gourieroux and J. Jasiak, “Multivariate Jacobi process with application to smooth transitions,” Journal of Econometrics, vol. 131, no. 1-2, pp. 475–505, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. S. S. Girimaji, “Assumed beta-pdf model for turbulent mixing: validation and extension to multiple scalar mixing,” Combustion Science and Technology, vol. 78, no. 4, pp. 177–196, 1991. View at Google Scholar
  11. M. Steinrucken, Y. X. Rachel Wang, and Y. S. Song, “An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection,” Theoretical Population Biology, vol. 83, pp. 1–14, 2013. View at Google Scholar
  12. C. W. Gardiner, Stochastic Methods, A Handbook For the Natural and Social Sciences, Springer, Berlin, Germany, 4th edition, 2009.
  13. J. Bakosi and J. R. Ristorcelli, “Exploring the beta distribution in variable-density turbulent mixing,” Journal of Turbulence, vol. 11, no. 37, pp. 1–31, 2010. View at Google Scholar
  14. J. L. Forman and M. Sørensen, “The Pearson diffusions: a class of statistically tractable diffusion processes,” Scandinavian Journal of Statistics, vol. 35, no. 3, pp. 438–465, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. S. B. Pope, “PDF methods for turbulent reactive flows,” Progress in Energy and Combustion Science, vol. 11, no. 2, pp. 119–192, 1985. View at Google Scholar
  16. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Third corrected printing, Springer, Berlin, Germany, 1999.
  17. S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, vol. 2, Academic Press, 1981.