Coarse graining from coarse-grained descriptions.

We present a generalization of Zwanzig's method of projection operators to the case where the underlying dynamics is not deterministic. The method allows us to perform a coarse graining of an already coarse-grained level of description in which fluctuations are important. The initial level of description is described by a Fokker-Planck equation and, under suitable approximations, the final slower level of description is also described by a Fokker-Planck equation. We illustrate the method for the simple case of the diffusion of colloidal particles at two levels of descriptions.