The Langevin equation is used to describe the Brownian motion of a particle in a fluid.
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:
- ,
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.
