Master equation and diffusion

Dividing these last two equations term by term, we obtain 

Taking the limits At — 0 and Az — 0 and keeping (Az)2 / At = 2V constant in the limiting case, the previous equation gives the diffusion equation (2.18) in one dimension. 

A good review of the master equation approach to chemical kinetics has been given by McQuarrie [383]. Jacquez [335] presents the master equation for the general ra-compartment, the catenary, and the mammillary models. That author further develops the equation for the one- and two-compartment models to obtain the expectation and variance of the number of particles in the model. Many others consider the m-compartment case [342,345,384], and Matis [385] gives a complete methodological rule to solve the Kolmogorov equations. 

We can, however, analyze these problems within the framework of the stochastic formulation by looking for an exact solution, or by using the probability generating functions, or the stochastic simulation algorithm. 

---