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Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions
2.	Creator	Author's name, affiliation, country	J. Armando Dominguez-Molina; Universidad Autónoma de Sinaloa; Mexico
2.	Creator	Author's name, affiliation, country	Víctor Pérez-Abreu; Centro de Investigación en Matemáticas; Mexico
2.	Creator	Author's name, affiliation, country	Alfonso Rocha-Arteaga; Universidad Autónoma de Sinaloa; Mexico
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Infinitely divisible random matrix, matrix subordinator, Bercovici-Pata bijection, matrix semimartingale, matrix compound Poisson.
3.	Subject	Subject classification	60B20; 60E07; 60G51; 60G57.
4.	Description	Abstract	It is known that the so-called Bercovici-Pata bijection can be explained in terms of certain Hermitian random matrix ensembles (Md)d≥1 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 (Md)d≥1.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-01-17
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/2113
10.	Identifier	Digital Object Identifier	10.1214/ECP.v18-2113
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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