  The homotopy analysis method known from its successful applications to obtain
quasi-analytical approximations of solutions of ordinary and partial
differential equations is applied to stochastic differential equations with
Gaussian stochastic forces and to the Fokker-Planck equations. Only the
simplest non-trivial examples of such equations are considered, but such that
they can almost immediately be translated to those which appear in the
stochastic quantization of a nonlinear scalar field theory. It has been found
that the homotopy analysis method yields excellent agreement with exact results
(when the latter are available) and appears to be a very promising approach in
the calculations related to quantum field theory and quantum statistical
mechanics.
