Asymptotic behavior of the nonparametric estimator for the renewal function associated with independent and nonstationary positive random variables

We estimate the renewal function, for independent and nonstationary positive random variables, by considering a sum of U-statistics or V-statistics. We study its asymptotic properties: asymptotic normality, almost sure convergence and weak convergence. This last property will be established on the space of functions defined on [0, 1] that are right-continuous and have left-hand limits, provided with the Skorokhod topology. (C) 2013 Academie des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.