The first use of the *Fokker-Planck* equation was the statistical description of Brownian motion of a particle in a fluid.

Brownian motion follows the Langevin equation, which can be solved for many differrent stochastic forcings with results being averaged (the Monte Carlo Method).

However, instead of this computationally intensive approach, one can use the Fokker-Planck equation and consider , that is, the probability density function of the particle having a velocity in the interval , when it starts its motion with at time .

The general form of the *Fokker-Planck equation for N variables* is

- ,