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2008 Hermite and Laguerre Polynomials and Matrix-Valued Stochastic Processes
Stephan Lawi
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Electron. Commun. Probab. 13: 67-84 (2008). DOI: 10.1214/ECP.v13-1353

Abstract

We extend to matrix-valued stochastic processes, some well-known relations between real-valued diffusions and classical orthogonal polynomials, along with some recent results about Lévy processes and martingale polynomials. In particular, joint semigroup densities of the eigenvalue processes of the generalized matrix-valued Ornstein-Uhlenbeck and squared Ornstein-Uhlenbeck processes are respectively expressed by means of the Hermite and Laguerre polynomials of matrix arguments. These polynomials also define martingales for the Brownian matrix and the generalized Gamma process. As an application, we derive a chaotic representation property for the eigenvalue process of the Brownian matrix.

Citation

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Stephan Lawi. "Hermite and Laguerre Polynomials and Matrix-Valued Stochastic Processes." Electron. Commun. Probab. 13 67 - 84, 2008. https://doi.org/10.1214/ECP.v13-1353

Information

Accepted: 5 February 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60144
MathSciNet: MR2386064
Digital Object Identifier: 10.1214/ECP.v13-1353

Subjects:
Primary: 60J60
Secondary: 15A52, 33C45, 60J65

JOURNAL ARTICLE
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