Estimates for the maximum modulus of analytic characteristic functions of probability laws on some sequences |
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| Author |
marta0691@rambler.ru, m_m_sheremeta@list.ru
Ivan Franko National University of Lviv
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| 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 $W_F$.
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| Keywords |
characteristic function; probability law; lower estimate
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| DOI |
doi:10.30970/ms.42.2.149-159
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| Reference |
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| Pages |
149-159
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| Volume |
42
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| Issue |
2
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| Year |
2014
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |