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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On infinitely divisible laws in $C[0,1]$
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by Aloisio Pessoa De Araujo PDF
Proc. Amer. Math. Soc. 51 (1975), 179-185 Request permission

Erratum: Proc. Amer. Math. Soc. 56 (1976), 393.

Abstract:

In Euclidean spaces, or in a separable Hilbert space, the characteristic function of an infinitely divisible distribution has the familiar form given by the LĂ©vy-Khintchine formula. The LĂ©vy measures $M$ of this formula are characterized by the property that the integral of $\min [1,||x|{|^2}]$ with respect to $M$ is finite. This simple situation no longer holds in the Banach space $C = C[0,1]$ where integrability of $\min [1,||x||]$ is sufficient but integrability of $\min [1,||x|{|^2}]$ is neither necessary nor sufficient. Certain other conditions which are sufficient to imply that $M$ is the LĂ©vy measure of a distribution on $C$ can be obtained with the use of an integral formula of Garsia.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 179-185
  • MSC: Primary 60B05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0407918-X
  • MathSciNet review: 0407918