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About the density of spectral measure of the two-dimensional SaS random vector

Marta Borowiecka-Olszewska, Jolanta K. Misiewicz (2003)

Discussiones Mathematicae Probability and Statistics

In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function e x p - ( | a | p + | b | p ) α / p 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].

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