Strong renewal theorem and local limit theorem in the absence of regular variation

Peter Kevei; Dalia Terhesiu

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arXiv · 2005.11121

Strong renewal theorem and local limit theorem in the absence of regular variation

Peter Kevei·Dalia Terhesiu

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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 a semistable law with index $\alpha\in (1/2,1]$. In the process we obtain local limit theorems for both finite and infinite mean, that is for the whole range $\alpha\in (0,2)$. We also derive the asymptotics of the renewal function for $\alpha\in (0,1]$.

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Peter Kevei, Dalia Terhesiu. 2020-05-22. Strong renewal theorem and local limit theorem in the absence of regular variation. https://arxiv.org/abs/2005.11121

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