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), 521-528

MSC:
Primary 60B11; Secondary 60F05

DOI:
https://doi.org/10.1090/S0002-9939-1987-0908661-9

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0908661-9

Keywords:
Operator stable laws,
moments,
pseudomoments,
domain of normal attraction,
exponents,
affine normalization

Article copyright:
© Copyright 1987
American Mathematical Society