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On free and classical type G distributions

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  • Department of Mathematical Sciences
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.
Original languageEnglish
JournalBrazilian Journal of Probability and Statistics
Volume24
Issue2
Pages (from-to)106-127
Number of pages22
ISSN0103-0752
DOIs
Publication statusPublished - 2010

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