The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. R. Askey and J. Wilson. A set of orthogonal polynomials that generalized the Racah coefficients or 6-$j$ symbols. SIAM Journal of Mathematical Analysis, 1979.
  2. Baker, T. H.; Forrester, P. J. The Calogero-Sutherland model and generalized classical polynomials. Comm. Math. Phys. 188 (1997), no. 1, 175--216. MR1471336 (99c:33012)
  3. M.F. Bru. Diffusions of perturbed principal component analysis. J. Multivariate Anal., 29:127--136, 1989.
  4. Bru, Marie-France. Processus de Wishart.(French) [The Wishart process] C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), no. 1, 29--32. MR0980317 (90f:60144)
  5. Bru, Marie-France. Wishart processes. J. Theoret. Probab. 4 (1991), no. 4, 725--751. MR1132135 (93b:60176)
  6. Chikuse, Yasuko. Properties of Hermite and Laguerre polynomials in matrix argument and their applications. Linear Algebra Appl. 176 (1992), 237--260. MR1183393 (93j:33003)
  7. Constantine, A. G. Some non-central distribution problems in multivariate analysis. Ann. Math. Statist. 34 1963 1270--1285. MR0181056 (31 #5285)
  8. Donati-Martin, Catherine; Doumerc, Yan; Matsumoto, Hiroyuki; Yor, Marc. Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws. Publ. Res. Inst. Math. Sci. 40 (2004), no. 4, 1385--1412. MR2105711 (2005k:60251)
  9. Dyson, Freeman J. A Brownian-motion model for the eigenvalues of a random matrix. J. Mathematical Phys. 3 1962 1191--1198. MR0148397 (26 #5904)
  10. Herz, Carl S. Bessel functions of matrix argument. Ann. of Math. (2) 61, (1955). 474--523. MR0069960 (16,1107e)
  11. Jack, Henry. A class of symmetric polynomials with a parameter. Proc. Roy. Soc. Edinburgh Sect. A 69 1970/1971 1--18. MR0289462 (44 #6652)
  12. James, Alan T. Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 1964 475--501. MR0181057 (31 #5286)
  13. A.T. James. Special Functions of matrix and single arguments in Statistics}. In Richard A. Askey, editor, Theory and Application of Special Functions, Academic Press, New York, 1964.
  14. R. Koekoek and R. Swarttouw. The Askey scheme of hypergeometric orthogonal polynomials and its q-analogue. Tech. report 98-17, Department of Technical Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands, 1998.
  15. König, Wolfgang; O'Connell, Neil. Eigenvalues of the Laguerre process as non-colliding squared Bessel processes. Electron. Comm. Probab. 6 (2001), 107--114 (electronic). MR1871699 (2002j:15025)
  16. Lassalle, Michel. Polynômes de Hermite généralisés.(French) [Generalized Hermite polynomials] C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 9, 579--582. MR1133488 (93a:33020)
  17. Lassalle, Michel. Polynômes de Jacobi généralisés.(French) [Generalized Jacobi polynomials] C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 6, 425--428. MR1096625 (92g:33019)
  18. Lassalle, Michel. Polynômes de Laguerre généralisés.(French) [Generalized Laguerre polynomials] C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 10, 725--728. MR1105634 (92g:33018)
  19. Lévy, Paul. The arithmetic character of the Wishart distribution. Proc. Cambridge Philos. Soc. 44, (1948). 295--297. MR0026261 (10,131a)
  20. Mehta, Madan Lal. Random matrices.Second edition.Academic Press, Inc., Boston, MA, 1991. xviii+562 pp. ISBN: 0-12-488051-7 MR1083764 (92f:82002)
  21. J.Meixner. Orthogonale Polynomsysteme mit einer besonderen gestalt der erzeugenden Funktion. J. London Math. Soc., 9:6--13, 1934.
  22. Muirhead, Robb J. Aspects of multivariate statistical theory.Wiley Series in Probability and Mathematical Statistics.John Wiley & Sons, Inc., New York, 1982. xix+673 pp. ISBN: 0-471-09442-0 MR0652932 (84c:62073)
  23. Schoutens, Wim. Stochastic processes and orthogonal polynomials.Lecture Notes in Statistics, 146. Springer-Verlag, New York, 2000. xiv+163 pp. ISBN: 0-387-95015-X MR1761401 (2001f:60095)
  24. I.M. Sheffer. Concerning Appell sets and associated linear functional equations. Duke Math. J., 3:593--609, 1937.
  25. Szegö, Gábor. Orthogonal polynomials.Fourth edition.American Mathematical Society, Colloquium Publications, Vol. XXIII.American Mathematical Society, Providence, R.I., 1975. xiii+432 pp. MR0372517 (51 #8724)
  26. Wong, Eugene. The construction of a class of stationary Markoff processes. 1964 Proc. Sympos. Appl. Math., Vol. XVI pp. 264--276 Amer. Math. Soc., Providence, R.I. MR0161375 (28 #4582)
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.