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Hermite and Laguerre Polynomials and Matrix-Valued Stochastic Processes


 
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1. Title Title of document Hermite and Laguerre Polynomials and Matrix-Valued Stochastic Processes
 
2. Creator Author's name, affiliation, country Stephan Lawi; KBC Financial Products Hong Kong Limited
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian matrices, Wishart processes, Hermite polynomials, Laguerre polynomials, martingale polynomials, chaos representation property
 
3. Subject Subject classification 60J60, 60J65, 15A52, 33C45
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Laboratoire de Probabilités et Modèles Aléatoires, CNRS-UMR 7599
 
7. Date (YYYY-MM-DD) 2008-02-05
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1353
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1353
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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