He extensively treats the problem of how to derive macroscopic rate equations from master equations, the method is a systematic expansion being called "Omega-expansion". Higher-order terms in the expansion can even be related to Langevin-like fluctuations.

In particular, a master equation is always a linear equation for the probability density P, whereas the resulting equation for the concentrations C can of course be non-linear.

In van Kampen's book, spatial dependence and diffusion is not explicitely treated, but this is straightforward.