Geodesic
On the asymptotics of the distribution of excess
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 292-299

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We find asymptotic expansion in the powers of $e^{-b}$ for the distribution of excess over boundary $b\to\infty$ under one-sided Cramér condition on the distribution of random walk summands. As a corollary, we obtain asymptotic expansion for the renewal function.
Keywords: random walk, excess over boundary, renewal function, asymptotic expansions. 
@article{SEMR_2015_12_a33,
     author = {V. I. Lotov},
     title = {On the asymptotics of the distribution of excess},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {292--299},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a33/}
}
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V. I. Lotov. On the asymptotics of the distribution of excess. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 292-299. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a33/