A stochastic derivation of the multivariate master equation describing reaction diffusion systems

We derive the multivariate master equation describing reaction diffusion systems from a discrete form master equation in phase space, assuming that the elastic collisions of the chemically active substances with the inert carrier gas have relaxed. In this state of collisional equilibrium the stochastic operator modelling the displacement of the particles between spatial cells reduces to the random wall operator and the reactive collision term yields the usual birth and death operator. Correlation functions are derived and their validity is discussed.