  On the basis of multivariate Langevin processes we present a realization of
Levy flights as a continuous process. For the simple case of a particle moving
under the influence of friction and a velocity dependent stochastic force we
explicitly derive the generalized Langevin equation and the corresponding
generalized Fokker-Planck equation describing Levy flights. Our procedure is
similar to the treatment of the Kramers-Fokker Planck equation in the
Smoluchowski limit. The proposed approach forms a feasible way of tackling Levy
flights in inhomogeneous media or systems with boundaries what is up to now a
challenging problem.
