Nonparametric estimators of solutions of renewal-type equations are proposed in terms of the empirical renewal function. Using the approach of Grübel and Pitts [Ann .Stat .21 1431 –1451 (1993)], who studied asymptotic properties of the empirical renewal function, a number of properties of our estimators are established, including strong consistency, asymptotic normality and efficiency, and asymptotic validity of bootstrap confidence bounds. The results are illustrated by some particular examples.
"Nonparametric estimation in renewal theory. II: Solutions of renewal-type equations." Ann. Statist. 28 (1) 88 - 115, February 2000. https://doi.org/10.1214/aos/1016120366