Asymptotics of a renewal-like recursion and an integral equation

TL;DR

This paper investigates the asymptotic behavior of solutions to a renewal-like recursion and an integral equation, demonstrating polynomial decay under broad conditions and extending classic results to more general coefficient and function forms.

Contribution

It establishes polynomial decay asymptotics for a generalized renewal-like recursion and integral equation, broadening the scope beyond traditional assumptions.

Findings

Solutions decay polynomially asymptotically

Results apply to more general coefficients and functions

Extends classic renewal theory results

Abstract

We consider a renewal-like recursion and prove that the solution is polynomially decaying asymptotically under suitable conditions. We prove similar results for the corresponding integral equation. In both cases coefficients and functions are of more general form than in the classic cases.