The density of particles in space or in phase space varies in time through continuous flow and through discrete jumps, due to collisions, chemical reactions, radio‐active decay, or births and deaths. A method is developed for computing the fluctuations arising from the random jumps and influenced by the flow. It equally applies to equilibrium, stationary states, and time‐dependent situations, both in linear and nonlinear systems. The method is based on the master equation and does not require the additional assumptions needed for the Langevin approach, although the correct form of the Langevin force can be deduced from it a posteriori. Factorial cumulants turn out to be a convenient tool. As applications the fluctuations inherent in the diffusion process are computed and a controversial chemical reaction is discussed.