Geodesic
Exact asymptotic behaviour of the renewal measure in the ``critical'' case
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 911-920.

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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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M. S. Sgibnev. Exact asymptotic behaviour of the renewal measure in the ``critical'' case. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 911-920. http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a15/

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