Spectral Decomposition for Generalized Domains of Semistable Attraction

Journal of Theoretical Probability

Volumn 10, Issue 1, 1997, Pages 51-71

  Meerschaert, Mark M ^a   Scheffler, Hans Peter ^b  

^a UNIVERSITY OF NEVADA   (United States)

^b TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Generalized domains of attraction; Operator semistable laws

Indexed keywords

EID: 0031476787     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022638213920     Document Type: Article

References (18)

1. Billingsley, P. (1966). Convergence of types in k-space, Z. Wahrsch. verw. Geb. 5, 175-179.
2. d, Th. Prob. Appl., pp. 703-705.
3. Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. II, 2nd Ed., Wiley, New York.
4. Hahn, M., and Klass, M. (1985). Affine normability of partial sums of i.i.d. random vectors: A characterization, Z. Wahrsch. verw. Geb. 69, 479-505.
5. Hirsch, M., and Smale, S. (1974). Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York.
6. Hudson, W., Veeh, J., and Weiner, D. (1988). Moments of distributions attracted to operator stable laws, J. Multivariate Anal. 24, 1-10.
7. N, Studia Math. 61, 29-39.
8. Meerschaert, M. (1984). Multivariate domains of attraction and regular variation, Doctoral Thesis, University of Michigan, Ann Arbor.
9. Meerschaert, M. (1990). Moments of random vectors which belong to some domain of normal attraction, Ann. Prob. 18, 870-876.
10. Meerschaert, M. (1991). Spectral decomposition for generalized domains of attraction, Ann. Prob. 19, 875-892.
11. k, Stat. Prob. Lett. 18, 233-239.
12. Meerschaert, M., and Scheffler, H. P. (1996a). Generalized domains of semistable attraction of nonnormal laws, J. Applied Anal. 2, 203-215.
13. Meerschaert, M., and Scheffler, H. P. (1996b). The structure of generalized domains of semistable attraction, Stat. Probab. Lett., to appear.
14. Phuc, H. (1994). Domains of operator semi-attraction of operator semistable probability measures, preprint.
15. Scheffler, H. P. (1994). Domains of semi-stable attraction of nonnormal semi-stable laws, J. Multivariate Anal. 51, 432-444.
16. Scheffler, H. P. (1995). Moments of distributions attracted to operator semi-stable laws, Stat. Prob. Lett. 24, 187-192.
17. Sharpe, M. (1969). Operator-stable probability distributions on vector groups, Trans. Amer. Math. Soc. 136, 51-65.
18. Seneta, E. (1976). Regularly Varying Functions, Lecture Notes in Mathematics, Vol. 508, Springer, Berlin.