There is a one-to-one correspondence between classical one-dimensional infinitely divisible distributions and free infinitely divisible distributions. In this work we study the free infinitely divisible distributions corresponding to the one-dimensional type G distributions. A new characterization of classical type G distributions is given first and the class of type A classical infinitely divisible distributions is introduced. The corresponding free type A distributions are studied and the role of a special symmetric beta distribution is shown as a building block for free type A distributions. It is proved that this symmetric beta distribution is the free multiplicative convolution of an arcsine distribution with the Marchenko–Pastur distribution.
Publié le : 2010-07-15
Classification:
Variance mixtures of Gaussian,
free infinite divisibility,
free compound Poisson distribution,
transformation of Lévy measures,
free multiplicative convolution
@article{1271770266,
author = {Arizmendi, Octavio and Barndorff-Nielsen, Ole E. and P\'erez-Abreu, V\'\i ctor},
title = {On free and classical type G distributions},
journal = {Braz. J. Probab. Stat.},
volume = {24},
number = {1},
year = {2010},
pages = { 106-127},
language = {en},
url = {http://dml.mathdoc.fr/item/1271770266}
}
Arizmendi, Octavio; Barndorff-Nielsen, Ole E.; Pérez-Abreu, Víctor. On free and classical type G distributions. Braz. J. Probab. Stat., Tome 24 (2010) no. 1, pp. 106-127. http://gdmltest.u-ga.fr/item/1271770266/