Authors: Voit, Michael
Title: Bessel convolutions on matrix cones
Other Titles: Algebraic properties and random walks
Language (ISO): en
Abstract: Bessel-type convolution algebras of measures on the matrix cones of positive semidefinite q × q-matrices over R,C,H were introduced recently by Rösler. These convolutions depend on a continuous parameter, generate commutative hypergroups and have Bessel functions of matrix argument as characters. In this paper, we study the algebraic structure of these hypergroups. In particular, the subhypergroups, quotients, and automorphisms are classified. The algebraic properties are partially related to properties of random walks on these 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 are presented. In particular, we obtain strong laws of large numbers and a central limit theorem with Wishart distributions as limits.
Subject Headings: Bessel functions of matrix argument
product formula
Wishart distributions
random walks on matrix cones
central limit theorem
strong laws of large numbers
Issue Date: 2008-10-23T13:25:03Z
Appears in Collections:Preprints der Fakultät für Mathematik

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