Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) real-space density, redshift-space and their geometric mean. We find that density PDF is well-described by function two parameters: $n_s$, spectral slope, $\sigma_L$, linear rms fluctuation. For mean real- densities, introduce third parameter, $s_L={\sqrt{\langle(dv^L_{\rm pec}/dr)^2...

Agreement with a conclusive experimental test is the ultimate requirement for establishing the validity of any theoretical proposal. However, discriminating experimentally among different alternatives is not always a straightforward matter. Indeed, under arbitrary experimental conditions it might be no possible to distinguish sufficiently among different conceivable alternatives as to guarantee...

In this paper, we show that the Chapman-Kolmogorov formula could be used as a recursive formula for computing the m-step-ahead conditional density of a Markov bilinear model. The stationary marginal probability density function of the model may be approximated by the m-step-ahead conditional density for sufficiently large m.