  We study a one-dimensional Markov modulated random walk with jumps. It is
assumed that amplitudes of jumps as well as a chosen velocity regime are random
and depend on a time spent by the process at a previous state of the underlying
Markov process.
  Equations for the distribution and equations for its moments are derived. We
characterise the martingale distributions in terms of observable proportions
between jump and velocity regimes.
