Asymptotics for Kendall’s renewal function

Abstract

An elementary renewal theorem and a Blackwell theorem provided by Jasiulis-Gołdyn 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. Our theoretical results are illustrated by several examples involving novel probability distributions and extremes.