Mathematics – Probability
Scientific paper
2008-09-09
Bernoulli 2011, Vol. 17, No. 3, 1095-1125
Mathematics
Probability
Published in at http://dx.doi.org/10.3150/10-BEJ305 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti
Scientific paper
10.3150/10-BEJ305
Multivariate versions of classical orthogonal polynomials such as Jacobi, Hahn, Laguerre and Meixner are reviewed and their connection explored by adopting a probabilistic approach. Hahn and Meixner polynomials are interpreted as posterior mixtures of Jacobi and Laguerre polynomials, respectively. By using known properties of gamma point processes and related transformations, a new infinite-dimensional version of Jacobi polynomials is constructed with respect to the size-biased version of the Poisson--Dirichlet weight measure and to the law of the gamma point process from which it is derived.
Griffiths Robert C.
Spanó Dario
No associations
LandOfFree
Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-209968