Brownian motion follows the Langevin equation, which can be solved for many different stochastic forcings with results being averaged (canonical ensemble in molecular dynamics). However, instead of this computationally intensive approach, one can use the Fokker–Planck equation and consider the probability p ( v , t ) d v of the particle having a velocity in the interval ( v , v + d v ) when it starts its motion with v 0 at time 0.