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Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 4, Pages 637–645 (Mi tvp2212)  

On asymmetric large deviations problem in the case of the stable limit law

A. V. Nagaev

Taškent

Abstract: Let $\xi_j$ be i. i. d. random variables such that for $x\ge x_0$
$$ \mathbf P\{\xi_1>x\}=x^{-\alpha}l(x),\quad\mathbf P\{\xi_1<-x\}=x^{-\beta}m(x), $$
where $0<\alpha<1$, $\beta>\alpha$ and the functions $l(x)$ and $m(x)$ vary slowly as $x\to\infty$. We study the asymptotic behaviour of
$$ \mathbf P\{\xi_1+…+\xi_n<x\}\quadfor x=0 (\inf\{y: ny^{-\alpha}l(y)\le 1\}). $$


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English version:
Theory of Probability and its Applications, 1984, 28:4, 670–680

Bibliographic databases:

Received: 08.06.1981

Citation: A. V. Nagaev, “On asymmetric large deviations problem in the case of the stable limit law”, Teor. Veroyatnost. i Primenen., 28:4 (1983), 637–645; Theory Probab. Appl., 28:4 (1984), 670–680

Citation in format AMSBIB
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\by A.~V.~Nagaev
\paper On asymmetric large deviations problem in the case of the stable limit law
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 4
\pages 637--645
\mathnet{http://mi.mathnet.ru/tvp2212}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=726890}
\zmath{https://zbmath.org/?q=an:0544.60037|0527.60027}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 4
\pages 670--680
\crossref{https://doi.org/10.1137/1128066}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TV66700002}


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