Fokker–Planck equation

Summary

The Fokker–Planck equation is the parabolic equation for the probability density of a diffusion process. Let $X_t$ solve a stochastic differential equation with drift $\mu$ and diffusion coefficient $\sigma$. Then its density $p(x, t)$ obeys a linear second-order equation built from $\mu$ and $\sigma\sigma^T$. Its spatial operator is the adjoint of the infinitesimal generator of the process, which is why it is also called the forward Kolmogorov equation. It links stochastic processes with partial differential equations.