A Remark on Local Behavior of Characteristic Functions
Maller, R. A.
Ann. Probab., Tome 2 (1974) no. 6, p. 1185-1187 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 1974-12-14
Classification:  Characteristic function,  local behavior,  distribution function,  asymptotic behavior,  regular variation 
@article{1176996507,
     author = {Maller, R. A.},
     title = {A Remark on Local Behavior of Characteristic Functions},
     journal = {Ann. Probab.},
     volume = {2},
     number = {6},
     year = {1974},
     pages = { 1185-1187},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996507}
}

Maller, R. A. A Remark on Local Behavior of Characteristic Functions. Ann. Probab., Tome 2 (1974) no. 6, pp.  1185-1187. http://gdmltest.u-ga.fr/item/1176996507/