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Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials
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Griffiths, Robert C. and Spanò, Dario (2011) Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials. Bernoulli , Vol.17 (No.3). pp. 1095-1125. doi:10.3150/10-BEJ305
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Official URL: http://www.bernoulli-society.org/index.php/publica...
Abstract
Multivariate versions of classical orthogonal polynomials such as Jacobi, Hahn, Laguerre,
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Orthogonal polynomials | ||||
Journal or Publication Title: | Bernoulli | ||||
Publisher: | International Statistical Institute | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.17 | ||||
Number: | No.3 | ||||
Page Range: | pp. 1095-1125 | ||||
DOI: | 10.3150/10-BEJ305 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 16 December 2015 | ||||
Date of first compliant Open Access: | 16 December 2015 |
Data sourced from Thomson Reuters' Web of Knowledge
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