Systematic method for solving transport equations derived from master equations

It is shown how a one-dimensional transport equation (derived from a master equation) for a time-dependent conditional average of an arbitrary function can be solved successively, if the moments of the transition probability can be expanded in a series of a special parameter. The transport equation for the time-dependent conditional average value can be transformed into a set of l linear partial differential equations of first order for the lth approximation of the conditional average value. The system of equations is closed in the sense that the lth partial differential equation is determined by the solutions of the l-1 partial differential equations. It is shown how the results obtained compare with the linear noise approximation. Two examples are chosen to illustrate the way to use the method. One is the classical example of the diffusion of a Brownian particle, the other is Alkemade's diode.