===== Fokker-Planck equation =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ n\in\mathbb N $ |
| @#55CCEE: context     | @#55CCEE: $ \mu:C(\mathbb R^n,\mathbb R^n) $ |
| @#55CCEE: context     | @#55CCEE: $ \mathsf{D}:C^2(\mathbb R^n,\mathbb R^{n^2}) $ |
| @#DDDDDD: range       | @#DDDDDD: $ ::\mu(\mathbf{x}) $ |
| @#DDDDDD: range       | @#DDDDDD: $ ::\mathsf{D}(\mathbf{x}) $ |

| @#FFBB00: definiendum | @#FFBB00: $ f \in \mathrm{it} $ |

| @#55EE55: postulate   | @#55EE55: $ f:C^2(\mathbb R^n\times\mathbb R,\mathbb R) $  |
| @#DDDDDD: range       | @#DDDDDD: $ ::f(\mathbf{x},t)  $ |

| @#55EE55: postulate   | @#55EE55: $ \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]]. 
==== Parents ====
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation|Fokker-Planck equation]]
=== Subset of ===
[[PDE system]]