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


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.


Download Citation

Stephan Lawi. "Hermite and Laguerre Polynomials and Matrix-Valued Stochastic Processes." Electron. Commun. Probab. 13 67 - 84, 2008.


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

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

Keywords: Brownian matrices , chaos representation property , Hermite polynomials , Laguerre polynomials , martingale polynomials , Wishart processes

Back to Top