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January, 2014 Riesz measures and Wishart laws associated to quadratic maps
Piotr GRACZYK, Hideyuki ISHI
J. Math. Soc. Japan 66(1): 317-348 (January, 2014). DOI: 10.2969/jmsj/06610317


We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset$ R$^n$ is a regular open convex cone. In this context we prove new general formulas for moments of the Wishart laws on non-symmetric cones. For homogeneous cases, all the quadratic maps are characterized and the associated Riesz measure and Wishart law with its moments are described explicitly. We apply the theory of relatively invariant distributions and a matrix realization of homogeneous cones obtained recently by the second author.


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Piotr GRACZYK. Hideyuki ISHI. "Riesz measures and Wishart laws associated to quadratic maps." J. Math. Soc. Japan 66 (1) 317 - 348, January, 2014.


Published: January, 2014
First available in Project Euclid: 24 January 2014

zbMATH: 1284.62314
MathSciNet: MR3161403
Digital Object Identifier: 10.2969/jmsj/06610317

Primary: 62H05
Secondary: 15B48 , 43A35

Keywords: convex cones , homogeneous cones , Riesz measures , Wishart laws

Rights: Copyright © 2014 Mathematical Society of Japan


Vol.66 • No. 1 • January, 2014
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