  For Kolmogorov equations associated to finite dimensional stochastic
differential equations (SDEs) in high dimension, a numerical method alternative
to Monte Carlo simulations is proposed. The structure of the SDE is inspired by
stochastic Partial Differential Equations (SPDE) and thus contains an
underlying Gaussian process which is the key of the algorithm. A series
development of the solution in terms of iterated integrals of the Gaussian
process is given, it is proved to converge - also in the infinite dimensional
limit - and it is numerically tested in a number of examples.
