Characterization of the Riesz Exponential Family on homogeneous cones

TL;DR

This paper characterizes the Riesz measure and Wishart exponential family on homogeneous cones by examining their invariance under the triangular group's action.

Contribution

It provides a new characterization theorem for the Riesz measure and Wishart family on homogeneous cones based on invariance properties.

Findings

Characterization theorem for Riesz measure on homogeneous cones

Identification of Wishart exponential family via invariance

Insights into the structure of exponential families on cones

Abstract

In the paper we present a characterization theorem of the Riesz measure and a Wishart exponential family on homogeneous cones through the invariance property of a natural exponential family under the action of the triangular group.