# Estimates for the maximum modulus of analytic characteristic functions of probability laws on some sequences

Author
Ivan Franko National University of Lviv
Abstract
Let $\varphi$ be the characteristic function of a probability law $F$ analytic in $\mathbb{D}_{R}$, $M(r,\varphi)=\max\{|\varphi(z)|\colon |z|=r\}$ and $W_F(x)=1-F(x)+F(-x)$, $x\geq 0$. We obtain upper estimates for $\mathop{\underline{\lim}}_{r\uparrow R}(\ln M(r,\varphi))/\Phi(r)$ for some positive convex on $(0,R)$ function $\Phi$ under certain conditions on $W_F$.
Keywords
characteristic function; probability law; lower estimate
Reference
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Pages
149-159
Volume
42
Issue
2
Year
2014
Journal
Matematychni Studii
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