  We demonstrate the equivalence of a Non--Markovian evolution equation with a
linear memory--coupling and a Fokker--Planck equation (FPE). In case the
feedback term offers a direct and permanent coupling of the current probability
density to an initial distribution, the corresponding FPE offers a non-trivial
drift term depending itself on the diffusion parameter. As the consequence the
deterministic part of the underlying Langevin equation is likewise determined
by the noise strength of the stochastic part. This memory induced stochastic
behavior is discussed for different initial distributions. The analytical
calculations are supported by numerical results.
