  A Fokker-Planck equation approach for the treatment of non-Markovian
stochastic processes is proposed. The approach is based on the introduction of
fictitious trajectories sharing with the real ones their local structure and
initial conditions. Different statistical quantities are generated by different
construction rules for the trajectories, which coincide only in the Markovian
case. The merits and limitations of the approach are discussed and applications
to transport in ratchets and to anomalous diffusion are illustated.
