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• W2952092178 abstract "Bessel-type convolution algebras of bounded Borel measures on the matrix cones of positive semidefinite $qtimes q$-matrices over $mathbb R, mathbb C, mathbb H$ were introduced recently by Rosler. These convolutions depend on some continuous parameter, generate commutative hypergroup structures and have Bessel functions of matrix argument as characters. Here, we first study the rich algebraic structure of these hypergroups. In particular, the subhypergroups and automorphisms are classified, and we show that each quotient by a subhypergroup carries a hypergroup structure of the same type. The algebraic properties are partially related to properties of random walks on matrix Bessel hypergroups. In particular, known properties of Wishart distributions, which form Gaussian convolution semigroups on these hypergroups, are put into a new light. Moreover, limit theorems for random walks on these hypergroups are presented. In particular, we obtain strong laws of large numbers and a central limit theorem with Wishart distributions as limits." @default.
• W2952092178 created "2019-06-27" @default.
• W2952092178 creator A5007679881 @default.
• W2952092178 date "2006-03-01" @default.
• W2952092178 modified "2023-09-27" @default.
• W2952092178 title "Bessel convolutions on matrix cones: Algebraic properties and random walks" @default.
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• W2952092178 hasPublicationYear "2006" @default.
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