Approximation of multidimensional stable densities
Journal of Multivariate Analysis
Multivariate stable distributions: approximation, estimation, simulation and identification
A practical guide to heavy tails
On two approaches to approximation of multidimensional stable laws
Journal of Multivariate Analysis
Journal of Multivariate Analysis
Estimation of stable spectral measures
Mathematical and Computer Modelling: An International Journal
Extrapolation of stable random fields
Journal of Multivariate Analysis
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It is known that each symmetric stable distribution in R^d is related to a norm on R^d that makes R^d embeddable in L"p([0,1]). In the case of a multivariate Cauchy distribution the unit ball in this norm is the polar set to a convex set in R^d called a zonoid. This work interprets symmetric stable laws using convex or star-shaped sets and exploits recent advances in convex geometry in order to come up with new probabilistic results for multivariate symmetric stable distributions. In particular, it provides expressions for moments of the Euclidean norm of a stable vector, mixed moments and various integrals of the density function. It is shown how to use geometric inequalities in order to bound important parameters of stable laws. Furthermore, covariation, regression and orthogonality concepts for stable laws acquire geometric interpretations.