Geodesic
Derivative of renewal density with infinite moment with $\alpha\in(0,1/2]$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 340-349

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Increments of the renewal function related to the distributions with infinite means and regularly varying tails of orders $\alpha\in(0,1]$ were described by Erickson [4,6]. However, explicit asymptotics for the increments are known for $\alpha\in(1/2,1]$ only. For smaller $\alpha$ one can get, generally speaking, only the lower limit of the increments. There are many examples showing that this statement cannot be improved in general. Topchii [1] refine Erikson's results by describing sufficient conditions for regularity of the renewal measure density of the distributions with regularly varying tails with $\alpha\in(0,1/2]$. Here we propose the conditions for regularity of the renewal measure density derivative.
Keywords: renewal measure density, regularly varying tails
Mots-clés : stable distributions. 
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     author = {V. A. Topchii},
     title = {Derivative of renewal density with infinite moment with $\alpha\in(0,1/2]$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {340--349},
     publisher = {mathdoc},
     volume = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a21/}
}
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V. A. Topchii. Derivative of renewal density with infinite moment with $\alpha\in(0,1/2]$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 340-349. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a21/