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Homotopy analysis method for stochastic differential equations

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.