In order to attain a statistical description of the evolution of cosmic density fluctuations in agreement with results from the numerical simulations, we introduce a probability conditional formalism (CF) based on an inventory of isolated overdense regions in a density random field. This formalism is a useful tool for describing at the same time the mass function (MF) of dark haloes, their mass aggregation histories (MAHs) and merging rates (MRs). The CF focuses on virialized regions in a self-consistent way rather than in mass elements, and it offers an economical description for a variety of random fields. Within the framework of the CF, we confirm that, for a Gaussian field, it is not possible to reproduce at the same time the MF, MAH, and MR of haloes, both for a constant and moving barrier. Then, we develop an inductive method for constraining the cumulative conditional probability from a given halo MF description, and thus, using the CF, we calculate the halo MAHs and MRs. By applying this method to the MF measured in numerical simulations by Tinker et al. 2008, we find that a reasonable solution, justified by a mass conservation argument, is obtained if ones introduce a rescaling -increment by ~30% - of the virial mass used in simulations and a (slight) deviation from Gaussianity. Thus, both the MAH and MR obtained by a Monte Carlo merger tree agree now with the predictions of numerical simulations. We discuss on the necessity of rescaling the virial mass in simulations when comparing with analytical approaches on the ground of the matter not accounted as part of the halos and the halo mass limit due to numerical. Our analysis supports the presence of a diffuse dark matter component that is not taken into account in the measured halo MFs inasmuch as it is not part of the collapsed structures.
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