Evolution of the cosmological density distribution function
  We present a new calculation for the evolution of the 1-point Probability Distribution Function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman-Kolmogorov equation and second-order Eulerian perturbation theory we propagate the initial density distribution into the nonlinear regime. Our calculations yield the moment generating function, allowing a straightforward derivation of the skewness of the PDF to second order. We find a new dependency on the initial perturbation spectrum. We compare our results with other approximations to the 1-pt PDF, and with N-body simulations. We find that our distribution accurately models the evolution of the 1-pt PDF of dark matter. 
Andrew Taylor and Peter Watts