Weak Solutions to the Stochastic Porous Media Equation via Kolmogorov   Equations: The Degenerate Case
  A stochastic version of the porous medium equation with coloured noise is studied. The corresponding Kolmogorov equation is solved in the space $L^2(H,\nu)$ where $\nu$ is an infinitesimally excessive measure. Then a weak solution is constructed. 
Viorel Barbu, Vladimir I. Bogachev, Giuseppe Da Prato, Michael   R\"ockner