The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem

Bartosz Kołodziejek. "The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem." Studia Mathematica 217.1 (2013): 1-17. <http://eudml.org/doc/285449>.

@article{BartoszKołodziejek2013,
abstract = {We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Wesołowski, Studia Math. 152 (2002), 147-160]. The main tool is a new solution of the Olkin-Baker functional equation on symmetric cones, under the assumption of continuity of respective functions. It was possible thanks to the use of Gleason's theorem.},
author = {Bartosz Kołodziejek},
journal = {Studia Mathematica},
keywords = {Wishart distribution; symmetric cones; independence; Gleason's theorem; functional equations},
language = {eng},
number = {1},
pages = {1-17},
title = {The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem},
url = {http://eudml.org/doc/285449},
volume = {217},
year = {2013},
}

TY - JOUR
AU - Bartosz Kołodziejek
TI - The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem
JO - Studia Mathematica
PY - 2013
VL - 217
IS - 1
SP - 1
EP - 17
AB - We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Wesołowski, Studia Math. 152 (2002), 147-160]. The main tool is a new solution of the Olkin-Baker functional equation on symmetric cones, under the assumption of continuity of respective functions. It was possible thanks to the use of Gleason's theorem.
LA - eng
KW - Wishart distribution; symmetric cones; independence; Gleason's theorem; functional equations
UR - http://eudml.org/doc/285449
ER -