Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2003 | 23 | 1 | 77-81
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
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].
  • Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
  • Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
  • [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.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.