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Fundam. Prikl. Mat., 2002, Volume 8, Issue 3, Pages 911–920 (Mi fpm682)  

Exact asymptotic behaviour of the renewal measure in the “critical” case

M. S. Sgibnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Let $\{S_{k}\}$ be a random walk drifting to $-\infty$. The exact asymptotic behaviour of $\sum\limits_{k=1}^{\infty}\mathsf P(S_{k}\geq x)$ is considered under the following moment conditions: for some $\gamma>0$, $\mathsf Ee^{\gamma S_{1}}=1$, $\mathsf E|S_{1}|e^{\gamma S_{1}}<\infty$ and, in general, $\mathsf ES_{1}^{2}e^{\gamma S_{1}}=\infty$.

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Bibliographic databases:
UDC: 519.218.4
Received: 01.05.2000

Citation: M. S. Sgibnev, “Exact asymptotic behaviour of the renewal measure in the “critical” case”, Fundam. Prikl. Mat., 8:3 (2002), 911–920

Citation in format AMSBIB
\Bibitem{Sgi02}
\by M.~S.~Sgibnev
\paper Exact asymptotic behaviour of the renewal measure in the ``critical'' case
\jour Fundam. Prikl. Mat.
\yr 2002
\vol 8
\issue 3
\pages 911--920
\mathnet{http://mi.mathnet.ru/fpm682}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1971881}
\zmath{https://zbmath.org/?q=an:1056.60088}


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  • Фундаментальная и прикладная математика
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