## Fokker-Planck equation

### Set

 context $n\in\mathbb N$ context $\mu:C(\mathbb R^n,\mathbb R^n)$ context $\mathsf{D}:C^2(\mathbb R^n,\mathbb R^{n^2})$ range $::\mu(\mathbf{x})$ range $::\mathsf{D}(\mathbf{x})$
 definiendum $f \in \mathrm{it}$
 postulate $f:C^2(\mathbb R^n\times\mathbb R,\mathbb R)$ range $::f(\mathbf{x},t)$
 postulate $\frac{\partial }{\partial t} f = -\mathrm{div} (\mu \cdot f) + \sum_{i=1}^{n} \sum_{j=1}^{n} \frac{\partial^2}{\partial x_i \, \partial x_j} (\mathsf{D}_{ij}\cdot f)$

### Discussion

Among other things, the Fokker-Planck equation also describes the evolution of the probability density of a Wiener process.