Asymptotics for Kendall's renewal function

TL;DR

This paper extends renewal theorems for Kendall convolutions to the Gamma class, providing weaker hypotheses and analyzing convergence rates of the limits involved.

Contribution

It weakens the assumptions of existing renewal theorems for Kendall convolutions and extends them to the Gamma class, including convergence rate analysis.

Findings

Renewal theorem and Blackwell theorem proved under weaker conditions

Extended to the Gamma class of distributions

Analyzed convergence rates of the limits

Abstract

An elementary renewal theorem and a Blackwell theorem provided by Jasiulis-Go{\l}dyn et al. (2020) in a setting of Kendall convolutions are proved under weaker hypothesis and extended to the Gamma class. Convergence rates of the limits concerned in these theorems are analyzed.