Characterization of the Wishart Distribution on Homogeneous Cones in the Bobecka and Wesolowski Way

Abstract

The aim of this article is to extend the characterization of the ordinary Wishart on symmetric matrices as given by Bobecka and Wesołowski (2002) to the Wishart distribution on homogeneous cones.

Keywords:

• Functional equation
• Homogeneous cone
• Vinberg algebra
• Wishart distribution

Mathematics Subject Classification:

• 60B11
• 60E05

Acknowledgments

I am very grateful to Abdelhamid Hassairi and Hélène Massam for many discussions on the subject of this article. I sincerely thank a referee for his suggestions and comments that led to significant improvements in the article.