Recall from Chapter 3 that a stochastic equation is a differential equation for a quantity whose rate of change contains a random component. One often refers to a quantity like this as being “driven by noise”, and the technical term for it is a stochastic process. So far we have found the probability density for a stochastic process by solving the stochastic differential equation for it. There is an alternative method, where instead one derives a partial differential equation for the probability density for the stochastic process. One then solves this equation to obtain the probability density as a function of time. If the process is driven by Gaussian noise, the differential equation for the probability density is called a Fokker–Planck equation.

Describing a stochastic process by its Fokker–Planck equation does not give one direct access to as much information as the Ito stochastic differential equation, because it does not provide a practical method to obtain the sample paths of the process. However, it can be used to obtain analytic expressions for steady-state probability densities in many cases when these cannot be obtained from the stochastic differential equation. It is also useful for an alternative purpose, that of describing the evolution of many randomly diffusing particles. This is especially useful for modeling chemical reactions, in which the various reagents are simultaneously reacting and diffusing.