  We provide new regularity results for the solutions of the Kolmogorov
equation associated to a SPDE with nonlinear diffusion coefficients and a
Burgers type nonlinearity. This generalizes previous results in the simpler
cases of additive or affine noise. The basic tool is a discrete version of a
two sided stochastic integral which allows a new formulation for the
derivatives of these solutions. We show that this can be used to generalize the
weak order analysis performed in [16]. The tools we develop are very general
and can be used to study many other examples of applications.

Probability;Analysis of PDEs