Strong Renewal Theorem and Local Limit Theorem in the Absence of Regular Variation

Péter Kevei () and Dalia Terhesiu ()
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Péter Kevei: University of Szeged
Dalia Terhesiu: University of Leiden

Journal of Theoretical Probability, 2022, vol. 35, issue 2, 1013-1048

Abstract: Abstract We obtain a strong renewal theorem with infinite mean beyond regular variation, when the underlying distribution belongs to the domain of geometric partial attraction of a semistable law with index $$\alpha \in (1/2,1]$$ α ∈ ( 1 / 2 , 1 ] . In the process we obtain local limit theorems for both finite and infinite mean, that is, for the whole range $$\alpha \in (0,2)$$ α ∈ ( 0 , 2 ) . We also derive the asymptotics of the renewal function for $$\alpha \in (0,1]$$ α ∈ ( 0 , 1 ] .

Keywords: Local limit theorem; Strong renewal theorem; Semistable law; 60K05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01081-w

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