Evolution of the cosmological density distribution function

We present a new calculation for the evolution of the one-point probability distribution function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman-Kolmogorov equation and seco nd-order Eulerian perturbation theory we propagate the initial density dist ribution into the non-linear regime. Our calculations yield the moment gene rating function, allowing a straightforward derivation of the skewness of t he PDF to second order. We find a new dependence on the initial perturbatio n spectrum. We compare our results with other approximations to the one-poi nt PDE and with N-body simulations. We find that our distribution accuratel y models the evolution of the one-point PDF of dark matter.