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

• Autorzy: Marta Borowiecka-Olszewska , Jolanta K. Misiewicz
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

stable; sub-stable; maximal stable random vector; spectral measure

Kategorie tematyczne

• 60E10: Characteristic functions; other transforms
• 60A10: Probabilistic measure theory
• 60E07: Infinitely divisible distributions; stable distributions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2003
• Tom: 23
• Numer: 1
• Strony: 77-81

Daty

wydano

2003

otrzymano

2003-04-07

Twórcy

autor

Marta Borowiecka-Olszewska

• Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

autor

Jolanta K. Misiewicz

• Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmps.1037