  The paper presents a multidimensional model for nonlinear Markovian random
walks that generalizes one we developed previously (Phys. Rev. E v.79, 011110,
2009) in order to describe the Levy type stochastic processes in terms of
continuous trajectories of walker motion. This approach may open a way to treat
Levy flights or Levy random walks in inhomogeneous media or systems with
boundaries in the future.
  The proposed model assumes the velocity of a wandering particle to be
affected by a linear friction and a nonlinear Langevin force whose intensity is
proportional to the magnitude of the velocity for its large values. Based on
the singular perturbation technique the corresponding Fokker-Planck equation is
analyzed and the relationship between the system parameters and the Levy
exponent is found. Following actually the previous paper we demonstrate also
that anomalously long displacements of the wandering particle are caused by
extremely large fluctuations in the particle velocity whose duration is
determined by the system parameters rather than the duration of the observation
interval. In this way we overcome the problem of ascribing to Levy random walks
non-Markov properties.
