V. A. Vatutin, V. A. Topchii, “A key renewal theorem for heavy tail distributions with <nobr>$\beta\in(0,0.5]$</nobr>”, Teor. Veroyatnost. i Primenen., 2013, Volume 58, Issue 2,Pages <nobr>387

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Short Communications

A key renewal theorem for heavy tail distributions with $\beta\in(0,0.5]$

V. A. Vatutin^a, V. A. Topchii^b

^a Steklov Mathematical Institute of the Russian Academy of Sciences
^b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: 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.

MSC: 60

Received: 29.02.2012

DOI: 10.4213/tvp4512