Geodesic
A key renewal theorem for heavy tail distributions with $\beta\in(0,0.5]$
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 387-396

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An asymptotic behavior of increments of the renewal functions generated by the distributions with tails varying at $\pm\infty$ regularly with index $\beta\in(0,0.5]$ is investigated.
Keywords: increments of renewal function; infinite Mean; stable law on the real line; nonlattice distribution; regularly varying functions. 
@article{TVP_2013_58_2_a9,
     author = {V. A. Vatutin and V. A. Topchii},
     title = {A key renewal theorem for heavy tail distributions with $\beta\in(0,0.5]$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {387--396},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a9/}
}
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V. A. Vatutin; V. A. Topchii. A key renewal theorem for heavy tail distributions with $\beta\in(0,0.5]$. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 387-396. http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a9/