Dynamics of a randomly kicked particle

Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of walker grows non-linearly with time contrast to diffusive motion described by random walks or Brownian motion. In this paper we study extension LW one dimension introducing correlation among velocities different (flight) steps. Such is absent model. The correlations are introduced making velocity at step dependent on previous addition usual noise ('kick') that particle gets intervals from surrounding medium Consequently dynamics position becomes non-Markovian. We statistical properties and t, both analytically numerically. show how choices distribution degree correlation, controlled parameter r, affect late behaviour these quantities.