Abstract : This paper considers statistical inference for the rate function of a recurrent event process. We study two semi-parametric models of event-specific types. These kind of models are stratified with respect to each event which allows more flexibility to fit the data. The first model studied in this paper was introduced by Prentice et al. and has a multiplicative form. The second one is based on the Aalen model introduced in the context of survival data and has an additive form. For reasonable sizes of sample in event-specific models the number of estimated parameters can be very large compared to the number of covariates. In order to remedy to this over-parametrization, a total-variation penalty is used which constrain some of the parameters to be constant. The asymptotic behavior of the penalized estimator is derived. Through a simulation study and analysis of real data, the performance of our estimator is compared with the unconstrained estimator and the Andersen and Gill constant estimator.