This article is cited in 1 paper

On Stone's renewal theorem for arithmetic distributions

M. S. Sgibnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The well-known Stone's renewal theorem is refined for the case of arithmetic distributions having at least one exponentially decreasing tail. A very general version of the renewal theorem for arithmetic distributions with a semi-multiplicative bound of the residual term is proved.

Keywords: renewal theorem, Stone's theorem, arithmetic distribution, semimultiplicative sequence.

UDC: 519.218.4

Received: 21.12.2016

DOI: 10.4213/dm1431

 English version: Discrete Mathematics and Applications, 2018, 28:6, 397–404

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