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.)References
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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