0n the Domain Of Attraction of Stable and of Extreme Value Distributions
In this note we give an elementary proof of a characterization for stability of multivariate distributions by considering a functional equation.
In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in [4].