Fokker-Planck (FP) equations, also known as Kolmogorov forward equations, are a central subject in the study of diffusion processes. FP equations describe the probability density function of a given observable (position, velocoty, etc) of a particle given its evolution in time.
In this repo, the numerical solution of the FP equation in large times is calculated.
Given a set of random variables Xi, we can generate a sistem of i differential equations. Since each individual particle executes a motion which is independent of the motions of all other particles, it is possible to paralelize numerical calculations by using one thread per equation of motion.
An stochastic dynamics can be written as an FP equation in the form
∂tP(x, t) = T ∂x^2 P(x, t) + ∂x[∂xV (x)P(x, t)],
with stationary solutions in large times
P(x, t → ∞) ∝ exp(−V (x)/T).