We propose a numerical solution for the solution of the
Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial
differential equations in Hilbert spaces.
The method is based on the spectral decomposition of the Ornstein-Uhlenbeck
semigroup associated to the Kolmogorov equation. This allows us to write the
solution of the Kolmogorov equation as a deterministic version of the
Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov
equation as a infinite system of ordinary differential equations, and by
truncation it we set a linear finite system of differential equations. The
solution of such system allow us to build an approximation to the solution of
the Kolmogorov equations. We test the numerical method with the Kolmogorov
equations associated with a stochastic diffusion equation, a Fisher-KPP
stochastic equation and a stochastic Burgers Eq. in dimension 1.Comment: 28 pages, 10 figure
