Nonlinear Fokker–Planck–Kolmogorov equations in Hilbert spaces

We study the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equations for probability measures on a Hilbert space, corresponding to stochastic partial differential equations. Sufficient conditions for the uniqueness of probability solutions for a cylindrical diffusion operator and for a possibly degenerate diffusion operator are given. A new general existence result is established without explicit growth restrictions on the coefficients.