Series representation for operator semistable laws and domains of normal attraction
This paper generalizes the so called Lepage series representation to operator semistable laws. A random vector \(Y\) with an operator semistable distribution \(\mu\) having no normal component is represented as an almost surely converging series of a function of simple random variables. These simple random variables are \(\Gamma\)-distributed random variables and random elements of the unit sphere obtained from the desintegration formula of the Lévy measure of \(\mu\). Furthermore the generalized domain of normal attraction of an operator semistable law having no normal component is characterized in terms of the convergence of order statistics relative to some polar-coordinate system obtained from an exponent of \(\mu\).
scientific article; zbMATH DE number 1289192