Let $P$ be a distribution on $R$ with a positive, finite mean. A constructive, unified version of the renewal theorem is proved. A routine method is provided with which one can compute, in principle at least, the point $x_0$ where the renewal measure $Q$ settles down. As a corollary, it is shown that $x_0$ depends continuously on $P$.
"A Constructive Renewal Theorem." Ann. Probab. 4 (4) 644 - 655, August, 1976. https://doi.org/10.1214/aop/1176996033