The class of type G distributions of Rd and related subclasses of infinitely divisible distribution

• Autorzy: Maejima M. , Rosiński J.
• Języki publikacji: EN

Abstrakty

EN

Classes of infinitely divisible distributions obtained by iteration of Gaus-sian randomization of Levy measures are introduced and studied. Their relation to Urbanik-Sato nested classes of selfdecomposable distributions is also established.

Słowa kluczowe

EN

infinite divisibility; selfdecomposable distribution; Levy measures

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 2
• Strony: 251--266
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Maejima M.

• Department of Mathematics, Keio University 3-14-1, Hiyoshi, Kohoku-ku Yokohama 223-8522, Japan

autor

Rosiński J.

• Department of Mathematics, University of Tennessee Knoxville, TN 37996, U.S.A.

Bibliografia

• [1] Z. Jurek (1990): On Levy (spectral) measures of integral form on Banach spaces, Probab. Math. Stat. 11, 139-148.
• [2] Z. Jurek and W. Vervaat (1983): A random integral representation for self-decomposable Banach space valued random variables, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 62, 247-262.
• [3] M. Maejima and J. Rosiński (2000): Type G distributions on Rd, Research Report, Department of Mathematics, Keio University, KSTS/RR-00/011. (http://www.math.keio.ac.jp/acad/Preprint/prep_e.htm)
• [4] J. Rosiński (1991): On a class of infinitely divisible processes represented as mixtures of Gaussian processes, in: Stable Processes and Related Topics, S. Cambanis et al. eds., Birkhauser.
• [5] K. Sato (1980): Class L of multivariate distributions and its subclasses, J. Multivar. Anal. 10, 207-232.
• [6] K. Sato (1998): Multivariate distributions with selfdecomposable projections, J. Korean Math. Soc. 35, 783-791.
• [7] K. Sato (1999): Levy Processes and Infinitely Divisible Distributions, Cambridge University Press.
• [8] K. Sato and M. Yamazato (1984): Operator-selfdecomposable distributions as limit distributions of Ornstein-Uhlenbeck type, Stoch. Proc. Appl. 17, 73-100.
• [9] D. N. Shanbhag and M. Sreehari (1977): On certain self-decomposable distributions, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 38, 217-222.
• [10] K. Urbanik (1969): Self-decomposable probability distributions on Rm, Zastos. Mat. 10, 91-97.
• [11] K. Urbanik (1972): Slowly varying sequences of random variables, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 20, 679-682.
• [12] K. Urbanik (1973): Limit laws for sequences of normed sums satisfying some stability conditions, in: Multivariate Analysis - III (P.R. Krishnaiah, ed.), Academic Press, 225-237.
• [13] V. M. Zolotarev (1958): Distribution of the superposition of infinitely divisible processes, Th. Probab. Appl. 3, 185-188.