Czasopismo
2002
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Vol. 22, Fasc. 2
|
253--258
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
An S α S random vector Xis β-substable, α < β ≤ 2, if Xd = Y Θ 1/β for some symmetric β-stable random vector Y Θ ≥ 0 a random variable with the Laplace transform exp{−tα/β}, Y and Θ are independent. We say that an S α S random vector is maximal if it is not β-substable for any β > α. In the paper we show that the ca,nonical spectral measure for every S α S, β-substablerandom vector X, β > α is equivalent to the Lebesgue measure on Sn−1.We show also that every such vector admits the representation X=Y+Z, where Y is an S α S sub-Gaussian random vector, Z is a maximal S α S random vector, Y and Z are independent. The last representation is not unique.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
253--258
Opis fizyczny
Biblogr. 6 poz.
Twórcy
autor
- University of Zielona Góra, ul. Szafrana, 65-246 Zielona Góra, Poland
autor
- Department of Applied Mathematics, Okayama University of Science, 700-0005 Okayama, Japan
Bibliografia
- [1] J. K. Misiewicz, Sub-stable and pseudo-isotropic processes. Connections with the geometry of sub-spaces of Lx-spaces, Dissertationes Math. 358 (1996).
- [2] G. Samorodnitsky and M. Taqqu, Stable non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall, London 1993.
- [3] Y. Sato, Distributions of stable random fields of Chentsov type, Nagoya Math. J. 123 (1991), pp. 119-139.
- [4] Y. Sato and S. Takenaka, On determinism of symmetric α-stable processes of generalized Chentsov type, in: Gaussian Random Fields, World Scientific, 1991, pp. 332-345.
- [5] S. Takenaka, Integral-geometric constructions of self-similar stable processes, Nagoya Math. J. 123 (1991), pp. 1-12.
- [6] S. Takenaka, On determinism of set-indexed SαS processes, in: Trends in Probability and Related Analysis 1999, World Scientific, 1999, pp. 285-290.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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