Domains of attraction of nonnormal operator-stable laws

Abstract

A sequence of independent, identically distributed random vectors X 1, X 2, X 3,… is said to belong to the domain of attraction of a random vector Y is there exist linear operators A n and constant vectors b n such that A n ( X 1,…, X n )+ b n converges in distribution to Y. We present a simple, necessary, and sufficient condition for the existence of such A n , B n in the case where Y has no normal component.