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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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