Some remarks on S alpha S, beta - substable random vectors

• Autorzy: Misiewicz J.K. , Takenaka S.
• Języki publikacji: EN

Abstrakty

EN

An S α S random vector X_is β-substable, α < β ≤ 2, if X^d = Y Θ ^1/β for some symmetric β-stable random vector Y Θ ≥ 0 a random variable with the Laplace transform exp{−t^α/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 S_n−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

EN

symmetricα-stable vector; substable distributions; spectral measure

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 2
• Strony: 253--258
• Opis fizyczny: Biblogr. 6 poz.

Twórcy

autor

Misiewicz J.K.

• University of Zielona Góra, ul. Szafrana, 65-246 Zielona Góra, Poland

autor

Takenaka S.

• 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.