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Processus stochastiques matriciels, systèmes de racines et probabilités non commutatives

Abstract : We investigate some aspects of some matrix-valued diffusions and use Harmonic analysis tools to answer some probabilistic questions. We start with the Laguerre process then study the radial Dunkl process which generalizes the eigenvalues process of these diffusions. Next, we define and study the free Jacobi process, which is the infinite dimensional limiting process of the complex Jacobi-matrix. The last chapter deals with large deviations principle for statistics of one-dimensional Jacobi processes.
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https://tel.archives-ouvertes.fr/tel-00192155
Contributor : Nizar Demni <>
Submitted on : Monday, November 26, 2007 - 10:33:57 PM
Last modification on : Wednesday, December 9, 2020 - 3:10:44 PM
Long-term archiving on: : Monday, April 12, 2010 - 5:13:01 AM

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  • HAL Id : tel-00192155, version 1

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Nizar Demni. Processus stochastiques matriciels, systèmes de racines et probabilités non commutatives. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2007. Français. ⟨tel-00192155⟩

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