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December, 1974 A Remark on Local Behavior of Characteristic Functions
R. A. Maller
Ann. Probab. 2(6): 1185-1187 (December, 1974). DOI: 10.1214/aop/1176996507

Abstract

It is shown that, if, for a distribution function $F, 1 - F(x) + F(-x)$ varies regularly at $\infty$ with exponent $\alpha, 0 > \alpha > -1$, then $|\operatorname{Im} \phi(t)| = O(I - \operatorname{Re} \phi(t)) (t \rightarrow 0)$, where $\phi$ is the characteristic function of $F$. Versions for $\alpha \leqq -1$ are also given.

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R. A. Maller. "A Remark on Local Behavior of Characteristic Functions." Ann. Probab. 2 (6) 1185 - 1187, December, 1974. https://doi.org/10.1214/aop/1176996507

Information

Published: December, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0292.60031
MathSciNet: MR358918
Digital Object Identifier: 10.1214/aop/1176996507

Keywords: asymptotic behavior , Characteristic function , distribution function , local behavior , regular variation

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 6 • December, 1974
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