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

   
@article{ECP2113,
	author = {J. Armando Dominguez-Molina and Víctor Pérez-Abreu and Alfonso Rocha-Arteaga},
	title = {Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {18},
	year = {2013},
	keywords = {Infinitely divisible random matrix, matrix subordinator, Bercovici-Pata bijection, matrix semimartingale, matrix compound Poisson.},
	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.
},
	pages = {no. 6, 1-14},
	issn = {1083-589X},
	doi = {10.1214/ECP.v18-2113},    
        url = {http://ecp.ejpecp.org/article/view/2113}}