A Matsumoto-Yor characterization for Kummer and Wishart random matrices
Bartosz Ko{\l}odziejek
TL;DR
This paper proves a conjecture characterizing matrix Kummer and Wishart distributions via independence properties and solves the related functional equation under weak assumptions.
Contribution
It provides a positive resolution to a conjecture on the characterization of matrix Kummer and Wishart laws and finds the general solution to the associated functional equation.
Findings
Confirmed the independence-based characterization of matrix Kummer and Wishart laws.
Derived the general solution to the functional equation related to the characterization.
Extended the understanding of distributional characterizations in matrix-valued probability.
Abstract
In the paper we resolve positively the conjecture on a characterization of matrix Kummer and Wishart laws through independence property, which was posed in [Koudou, Statist. Probab. Lett. 82 (2012), 1903--1907] . Apart from the probabilistic result, we determine the general solution of the functional equation associated to the characterization problem under weak assumptions.
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