Comportement asymptotique de lʼestimateur non paramétrique de la fonction de renouvellement associée à des variables aléatoires positives stationnaires β-mélangeantes

To estimate the renewal function, for stationary β-mixing positive random variables, we consider a finite sum of empirical distribution functions. We study its asymptotics properties: asymptotic normality, almost surely convergence, and weak convergence. This last result 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.