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The contribution deals with a stochastic process cumulating random increments at random moments (the compound point process). First, its martingale - compensator decomposition is recalled. Then a multiplicative form of the model with the regression on covariates, simultaneously for the intensity of counting process and for the distribution of increments, is considered. Finally, a semi-parametric model is studied, the uniform consistency of estimators and the asymptotic normality of the process of residuals are proved.