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Riesz measures and Wishart laws associated to quadratic maps. (English) Zbl 1284.62314

Summary: 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 by the second author [see ibid. 52, No. 1, 161–186 (2000; Zbl 0954.43003)].

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
15B48 Positive matrices and their generalizations; cones of matrices
43A99 Abstract harmonic analysis

Citations:

Zbl 0954.43003
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References:

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