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| - | ===== Fokker-Planck equation ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $ n\in\mathbb N $ | | ||
| - | | @#88DDEE: $ \mu:C(\mathbb R^n,\mathbb R^n) $ | | ||
| - | | @#88DDEE: $ D:C^2(\mathbb R^n,\mathbb R^{n^2}) $ | | ||
| - | | @#DDDDDD: $ ::\mu(\mathbf{x}) $ | | ||
| - | | @#DDDDDD: $ ::\mathsf{D}(\mathbf{x}) $ | | ||
| - | | @#FFBB00: $ f \in \mathrm{it} $ | | ||
| - | |||
| - | | @#55EE55: $ f:C^2(\mathbb R^n\times\mathbb R,\mathbb R) $ | | ||
| - | | @#DDDDDD: $ ::f(\mathbf{x},t) $ | | ||
| - | |||
| - | | @#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]] | ||
