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For Kolmogorov equations associated to finite dimensional stochasticdifferential equations (SDEs) in high dimension, a numerical method alternativeto Monte Carlo simulations is proposed. The structure of the SDE is inspired bystochastic Partial Differential Equations (SPDE) and thus contains anunderlying Gaussian process which is the key of the algorithm. A seriesdevelopment of the solution in terms of iterated integrals of the Gaussianprocess is given, it is proved to converge - also in the infinite dimensionallimit - and it is numerically tested in a number of examples.

A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis