On the existence and convergence of pseudomoments for variables in the domain of normal attraction of an operator stable distribution
Author:
Daniel Charles Weiner
Journal:
Proc. Amer. Math. Soc. 101 (1987), 521528
MSC:
Primary 60B11; Secondary 60F05
MathSciNet review:
908661
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Abstract: Integrals are constructed to replace absolute moments for variables in the domain of normal attraction of an operator stable law. These integrals, called pseudomoments, improve on the geometric information contained in absolute moments. Existence and convergence to appropriate values of these integrals are shown for the variables and their affine normalized sums.
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 Chung, (1974) A course in probability theory, Academic Press, New York. MR 0346858 (49:11579)
 [W]
 Feller, (1971) An introduction to probability theory and its applications, Vol. II, Wiley, New York. MR 0270403 (42:5292)
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 Hahn and W. Hudson, (1987) Operator stable laws: Series representations and domains of normal attraction, Preprint.
 [M]
 Hahn and M. Klass, (1985) Affine normability of partial sums of i.i.d. random vectors: A characterization, Z. Wahrsch. Verw. Gebiete 69, 479505. MR 791908 (87f:60031)
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 Holmes, W. Hudson, and D. Mason, (1982) Operatorstable laws: Multiple exponents and elliptical symmetry, Ann. Probab. 3, 602612. MR 659531 (83i:60012)
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 Hudson, Z. Jurek, and J. Veeh, (1986) The symmetry group and exponents of operator stable probability measures, Ann. Probab. 3, 10141023. MR 841601 (89b:60093)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198709086619
PII:
S 00029939(1987)09086619
Keywords:
Operator stable laws,
moments,
pseudomoments,
domain of normal attraction,
exponents,
affine normalization
Article copyright:
© Copyright 1987
American Mathematical Society
