Langevin equation

Instead of looking at the variation of velocity over time, as in the Wiener equation, the Langevin equation deals with the temporal change in acceleration due to a stochastic[?] force:

<math>\mathbf{a} = \frac{d\mathbf{v}}{dt} = - \beta \mathbf{v} + \frac{F'(t)}{m} + \frac{F}{m}</math>,

where <math>- \beta \mathbf{v}</math> is friction (Stokes' law) and F' is the stochastic force.

If the stochastic force is zero, the system is deterministic, otherwise solutions can be obtained either by the Monte Carlo Method, i.e. simulating a statistical ensemble with different forcings and averaging, and statistically with the Fokker-Planck equation, which computes the change of probability density[?] over time.