On the Lukacs property for free random variables
Studia Mathematica (2015)
- Volume: 228, Issue: 1, page 55-72
- ISSN: 0039-3223
Access Full Article
top
Abstract
topHow to cite
topKamil Szpojankowski. "On the Lukacs property for free random variables." Studia Mathematica 228.1 (2015): 55-72. <http://eudml.org/doc/285405>.
@article{KamilSzpojankowski2015,
abstract = {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.},
author = {Kamil Szpojankowski},
journal = {Studia Mathematica},
keywords = {Lukacs characterization; free Poisson distribution; free cumulants; free gamma distribution},
language = {eng},
number = {1},
pages = {55-72},
title = {On the Lukacs property for free random variables},
url = {http://eudml.org/doc/285405},
volume = {228},
year = {2015},
}
TY - JOUR
AU - Kamil Szpojankowski
TI - On the Lukacs property for free random variables
JO - Studia Mathematica
PY - 2015
VL - 228
IS - 1
SP - 55
EP - 72
AB - 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.
LA - eng
KW - Lukacs characterization; free Poisson distribution; free cumulants; free gamma distribution
UR - http://eudml.org/doc/285405
ER -
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.