MEAN EXIT TIMES FOR FREE INERTIAL STOCHASTIC-PROCESSES

We study the mean exit time of a free inertial random process from a r egion in space. The acceleration alternatively takes the values +a and -a for random periods of time governed by a common distribution psi(t ). The mean exit time satisfies an integral equation that reduces to a partial differential equation if the random acceleration is Markovian . Some qualitative features of the behavior of the system are discusse d and checked by simulations. Among these features, the most striking is the discontinuity of the mean exit time as a function of the initia l conditions.