  We consider a stochastic differential equation in a Hilbert space with
time-dependent coefficients for which no general existence and uniqueness
results are known. We prove, under suitable assumptions, existence and
uniqueness of a measure valued solution, for the corresponding Fokker--Planck
equation. In particular, we verify the Chapman--Kolmogorov equations and get an
evolution system of transition probabilities for the stochastic dynamics
informally given by the stochastic differential equation.
