Mean first passage times of processes driven by white shot noise

We consider mean first passage times in systems driven by white shot noise with exponentially distributed jump heights. Simple interpretable results are obtained and the linkage between those results and the steady state probability density function of the process is presented. The virtual waiting-time or Takacs process (constant, losses) and the shot noise process with linear losses are analyzed in depth, along with a more complex process with useful implications for the modeling of the soil moisture dynamics in hydrology.