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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Regularly varying sequences
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by J. Galambos and E. Seneta PDF
Proc. Amer. Math. Soc. 41 (1973), 110-116 Request permission

Abstract:

A simple necessary and sufficient condition is developed for a sequence $\{ \theta (n)\} ,n = 0,1,2, \cdots$, of positive terms, to satisfy $\theta (n) = R(n),n \geqq 0$, where $R( \cdot )$ is a regularly varying function on $[0,\infty )$. The condition (2.1), below, leads to a Karamata-type exponential representation for $\theta (n)$. Various associated difficulties are also discussed. (The results are of relevance in connection with limit theorems in various branches of probability theory.)
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 41 (1973), 110-116
  • MSC: Primary 26A12
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0323963-5
  • MathSciNet review: 0323963