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Abstrakty
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
Wydawca
Czasopismo
Rocznik
Tom
Strony
251--266
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Department of Mathematics, Keio University 3-14-1, Hiyoshi, Kohoku-ku Yokohama 223-8522, Japan
autor
- 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.
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Bibliografia
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bwmeta1.element.baztech-article-PWA1-0038-0013