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

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.

13 pages

References in corpus (2)

• Extension of the Olkin and Rubin Characterization to the Wishart distribution on homogeneous cones
• The Lukacs theorem and the Olkin-Baker equation

Cited by in corpus (5)

• The Lukacs-Olkin-Rubin theorem on symmetric cones without invariance of the "quotient"
• Dual Lukacs regressions for non-commutative variables
• Multiplicative Cauchy functional equation on symmetric cones
• The Matsumoto--Yor Property and Its Converse on Symmetric Cones
• A Matsumoto-Yor characterization for Kummer and Wishart random matrices