Dynamics and density evolution in piecewise deterministic growth   processes
  A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability. 
Michael C. Mackey and Marta Tyran-Kaminska