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

Author 
marta0691@rambler.ru, m_m_sheremeta@list.ru
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 $W_F(x)=1F(x)+F(x)$, $x\geq 0$. 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 
149159

Volume 
42

Issue 
2

Year 
2014

Journal 
Matematychni Studii

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