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