On the Lukacs property for free random variables

Kamil Szpojankowski

Studia Mathematica, Tome 231 (2015), p. 55-72 / Harvested from The Polish Digital Mathematics Library

Résumé

The Lukacs property of the free Poisson distribution is studied. We prove that if free and are free Poisson distributed with suitable parameters, then + and ${(+)}^{- 1 / 2} {(+)}^{- 1 / 2}$ are free. As an auxiliary result we compute the joint cumulants of and $^{- 1}$ for free Poisson distributed . We also study the Lukacs property of the free Gamma distribution.

Publié le : 2015-01-01

Zbl 06497980

EUDML-ID : urn:eudml:doc:285405

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     title = {On the Lukacs property for free random variables},
     journal = {Studia Mathematica},
     volume = {231},
     year = {2015},
     pages = {55-72},
     zbl = {06497980},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-1-6}
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Kamil Szpojankowski. On the Lukacs property for free random variables. Studia Mathematica, Tome 231 (2015) pp. 55-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-1-6/