Fokker-Planck Equation

$d{X}_t=\mu (X_t,t)dt+\sigma (X_t,t)d{W}_t$ where

• $\mu$ defines the drift term
• $D(X_t,t):=\frac{1}{2}{\sigma }^2(X_t,t)$ is the diffusion coefficient

Letting $p(x,t)$ be the probability density function for $X_t$, we get the equivalent formulation $\frac{\partial }{\partial t}p(x,t)=-\frac{\partial }{\partial t}\left[\mu (x,t)p(x,t)\right]+\frac{{\partial }^2}{\partial x^2}\left[D(x,t)p(x,t)\right]$.