By reading Heinz-Peter Breuer: A Piece Wise Deterministic Process (where you have a deterministic time-evolution + a jump process and which is just a particular type of stochastic process) may be defined in terms of a Liouville master equation for its probability density : Where the first term is the deterministic term and the second term is the jump term. So my questions are : 1. ##P[\psi,t] ## is a probability functional so its a function of the wave function which is a function of what? time? 2. Is it also possible to relate this to the Lindblad Quantum Master Equation which is the most general master equation for an open Markovian system?