Geodesic
About the density of spectral measure of the two-dimensional SaS random vector
Discussiones Mathematicae. Probability and Statistics, Tome 23 (2003) no. 1, pp. 77-81.

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In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function exp-(|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].
Keywords: stable, sub-stable, maximal stable random vector, spectral measure 
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Borowiecka-Olszewska, Marta; Misiewicz, Jolanta. About the density of spectral measure of the two-dimensional SaS random vector. Discussiones Mathematicae. Probability and Statistics, Tome 23 (2003) no. 1, pp. 77-81. http://geodesic.mathdoc.fr/item/DMPS_2003_23_1_a3/

[1] P. Billingsley, Probability and Measure, John Wiley Sons, New York 1979.

[2] W. Feller, An Introduction to Probability Theory and its Applications, vol. 2, John Wiley Sons, New York 1966.

[3] R. Grzaślewicz and J.K. Misiewicz, Isometric embeddings of subspaces of Lα-spaces and maximal representation for symmetric stable processes, Functional Analysis (1996), 179-182.

[4] J.K. Misiewicz and S. Takenaka, Some remarks on SαS, β-sub-stable random vectors, preprint.

[5] J.K. Misiewicz, Sub-stable and pseudo-isotropic processes. Connections with the geometry of sub-spaces of Lα -spaces, Dissertationes Mathematicae CCCLVIII, 1996.

[6] J.K. Misiewicz and Cz. Ryll-Nardzewski, Norm dependent positive definite functions and measures on vector spaces, Probability Theory on Vector Spaces IV, ańcut 1987, Springer Verlag LNM 1391, 1989, 284-292.

[7] G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman Hall, London 1993.