Comportement asymptotique de lʼestimateur non paramétrique de la fonction de renouvellement associée à des variables aléatoires positives indépendantes et non stationnaires

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.