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

Marta Borowiecka-Olszewska; Jolanta K. Misiewicz

Discussiones Mathematicae Probability and Statistics (2003)

  • Volume: 23, Issue: 1, page 77-81
  • ISSN: 1509-9423

Abstract

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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 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].

How to cite

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Marta Borowiecka-Olszewska, and Jolanta K. Misiewicz. "About the density of spectral measure of the two-dimensional SaS random vector." Discussiones Mathematicae Probability and Statistics 23.1 (2003): 77-81. <http://eudml.org/doc/287633>.

@article{MartaBorowiecka2003,
abstract = {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].},
author = {Marta Borowiecka-Olszewska, Jolanta K. Misiewicz},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {stable; sub-stable; maximal stable random vector; spectral measure},
language = {eng},
number = {1},
pages = {77-81},
title = {About the density of spectral measure of the two-dimensional SaS random vector},
url = {http://eudml.org/doc/287633},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Marta Borowiecka-Olszewska
AU - Jolanta K. Misiewicz
TI - About the density of spectral measure of the two-dimensional SaS random vector
JO - Discussiones Mathematicae Probability and Statistics
PY - 2003
VL - 23
IS - 1
SP - 77
EP - 81
AB - 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].
LA - eng
KW - stable; sub-stable; maximal stable random vector; spectral measure
UR - http://eudml.org/doc/287633
ER -

References

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  1. [1] P. Billingsley, Probability and Measure, John Wiley & Sons, New York 1979. Zbl0411.60001
  2. [2] W. Feller, An Introduction to Probability Theory and its Applications, vol. 2, John Wiley & Sons, New York 1966. Zbl0138.10207
  3. [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. Zbl0890.46021
  4. [4] J.K. Misiewicz and S. Takenaka, Some remarks on SαS, β-sub-stable random vectors, preprint. 
  5. [5] J.K. Misiewicz, Sub-stable and pseudo-isotropic processes. Connections with the geometry of sub-spaces of Lα -spaces, Dissertationes Mathematicae CCCLVIII, 1996. Zbl0858.46008
  6. [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. [7] G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall, London 1993. Zbl0925.60027

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