Continuous-time ballistic process with random resets

We consider ballistic motion on the line with random velocity which at certain random epochs of time is reset to its starting position. The mobile then restarts from scratch with new velocity, sampled with a certain probability distribution, until the next reset occurs. The distribution for the hitting time to an arbitrary level is obtained. Inversion of the relevant Laplace transform is discussed under particular choices for the distribution of velocities and resets train and classified in terms of the weights of reset and velocities tails. The large time behavior of the running-maximum is considered. (paper: classical statistical mechanics, equilibrium and non-equilibrium)