(eng): The notion of the counting process is recalled and the ideaof the cumulative process, the stochastic process which cumulates random increments at random moments, is presented. We derive the martingale - compensator decomposition of the process, then we prove the uniform consistency of the estimator of the rate of cumulation and the asymptotic normality of the process of residuals. On this basis, the goodness-of-fit test and the test of homogeneity are proposed.