Alternative conditions for attraction to stable vectors

• Autorzy: de Haan L. , Li D. , Peng L. , Iglesias-Pereira H.
• Języki publikacji: EN

Abstrakty

EN

Relying on Geluk and de Haan [3] we derive alternative necessary and sufficient conditions for the domain of attraction of a stable distribution in R^d which are phrased entirely in terms of (joint distributions of) linear combinations of the marginals. The conditions in terms of characteristic functions should be useful for determining rates of convergence, as in de Haan and Peng [4].

Słowa kluczowe

EN

characteristic function; domain of attraction; regularly varying; stable vector

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 2
• Strony: 303--317
• Opis fizyczny: Biblogr. 6 poz.

Twórcy

autor

de Haan L.

• Econometric Institute Erasmus, University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

autor

Li D.

• Econometric Institute Erasmus, University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

autor

Peng L.

• School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332-0160, U.S.A.

autor

Iglesias-Pereira H.

• DEIO/Faculdade de Ciencias,CEAUL/Centro de Estatistica e Aplicacoes, Universidade de Lisboa, 1749-016 Lisboa, Portugal

Bibliografia

• [1] B. Basrak, R. A. Davis and T. Mikosch, A characterization of multivariate regular variation, Ann. Appl. Probab. (2000).
• [2] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York 1971.
• [3] J. L. Geluk and L. de Ha an, Stable probability distributions and their domains of attraction: a direct approach, Probab. Math. Statist. 20 (1) (2000), pp. 169-188.
• [4] L. de Haan and L, Peng, Exact rates of convergence to a stable law, J. London Math. Soc. (2) 59 (1999), pp. 1134-1152.
• [5] E. L. Rvaceva, On domains of attraction of multi-dimensional distributions, Select. Transi. Math. Statist. Probab. 2 (1962), pp. 183-205.
• [6] G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall, London 1994.