  A perturbative method for solving the Langevin equation of inflationary
cosmology in presence of backreaction is presented. In the Gaussian
approximation, the method permits an explicit calculation of the probability
distribution of the inflaton field for an arbitrary potential, with or without
the volume effects taken into account. The perturbative method is then applied
to various concrete models namely large field, small field, hybrid and running
mass inflation. New results on the stochastic behavior of the inflaton field in
those models are obtained. In particular, it is confirmed that the stochastic
effects can be important in new inflation while it is demonstrated they are
negligible in (vacuum dominated) hybrid inflation. The case of stochastic
running mass inflation is discussed in some details and it is argued that
quantum effects blur the distinction between the four classical versions of
this model. It is also shown that the self-reproducing regime is likely to be
important in this case.
