Cosmic mass functions from Gaussian stochastic diffusion processes

Gaussian stochastic diffusion processes are used to derive cosmic mass func tions. To get analytic relations previous studies exploited the sharp k-spa ce filter assumption yielding zero drift terms in the corresponding Fokker- Planck (Kolmogorov's forward) equation and thus simplifying analytic treatm ents significantly (excursion set formalism). In the present paper methods are described to derive for given diffusion processes and Gaussian random f ields the corresponding mass and filter functions by solving the Kolmogorov 's forward and backward equations including nonzero drift terms. This forma lism can also be used in cases with non-sharp k-space filters and for diffu sion processes exhibiting correlations between different mass scales.