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Transactions of the American Mathematical Society

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On tails and domains of attraction of stable measures in Banach spaces


Authors: Aloisio Araujo and Evarist Giné
Journal: Trans. Amer. Math. Soc. 248 (1979), 105-119
MSC: Primary 60B12
DOI: https://doi.org/10.1090/S0002-9947-1979-0521695-1
MathSciNet review: 521695
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Abstract: The exact tail behavior of stable measures in Banach spaces and measures in their domains of attraction is given. Conditions for a p.m. to be in the domain of attraction of a stable p.m. of order $ \alpha$ are derived which are sufficient in type p spaces, $ p > \alpha $, and necessary in general. This paper also contains a short proof of the Lévy-Khinchin formula in Banach spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0521695-1
Keywords: Domains of attraction, stable laws, tails of stable laws, Lévy-Khinchin representation
Article copyright: © Copyright 1979 American Mathematical Society

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