BALLISTIC LEVY WALK WITH RESTS: ESCAPE FROM A BOUNDED DOMAIN

The Levy walk model that takes into account a waiting of a walker between consecutive displacements is analysed. The motion is restricted to a finite region, bounded by two absorbing barriers, and quantities describing the escape from this region are determined. Simple expression for a mean first passage time is derived for a ballistic version of the Levy walk. Two limits emerge from the model: of short waiting time, that corresponds to Levy walks without rests, and long waiting time which exhibits properties of a Levy flights model. The analytical results are compared with Monte Carlo trajectory simulations.