## The Annals of Probability

### A Remark on Local Behavior of Characteristic Functions

R. A. Maller

#### 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.

#### Article information

Source
Ann. Probab., Volume 2, Number 6 (1974), 1185-1187.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996507

Digital Object Identifier
doi:10.1214/aop/1176996507

Mathematical Reviews number (MathSciNet)
MR358918

Zentralblatt MATH identifier
0292.60031

JSTOR