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2013 Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions
J. Armando Dominguez-Molina, Víctor Pérez-Abreu, Alfonso Rocha-Arteaga
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Electron. Commun. Probab. 18: 1-14 (2013). DOI: 10.1214/ECP.v18-2113

Abstract

It is known that the so-called Bercovici-Pata bijection can be explained in terms of certain Hermitian random matrix ensembles (M<sub>d</sub>)<sub>d≥1</sub> whose asymptotic spectral distributions are free infinitely divisible. We investigate Hermitian Lévy processes with jumps of rank one associated to these random matrix ensembles introduced by Benaych-Georges and Cabanal-Duvillard. A sample path approximation by covariation processes for these matrix Lévy processes is obtained. As a general result we prove that any d×d complex matrix subordinator with jumps of rank one is the quadratic variation of a $\mathbb{C}^d$-valued Lévy process. In particular, we have the corresponding result for matrix subordinators with jumps of rank one associated to the random matrix ensembles (M<sub>d</sub>)<sub>d≥1</sub>.<br />

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J. Armando Dominguez-Molina. Víctor Pérez-Abreu. Alfonso Rocha-Arteaga. "Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions." Electron. Commun. Probab. 18 1 - 14, 2013. https://doi.org/10.1214/ECP.v18-2113

Information

Accepted: 17 January 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1308.60056
MathSciNet: MR3019669
Digital Object Identifier: 10.1214/ECP.v18-2113

Subjects:
Primary: 60B20
Secondary: 60E07, 60G51, 60G57

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