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 fokker-planck_equation [2013/09/17 14:32]nikolaj fokker-planck_equation [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/17 14:32 nikolaj 2013/09/17 14:32 nikolaj 2013/09/17 14:31 nikolaj 2013/09/17 14:30 nikolaj 2013/09/17 14:28 nikolaj 2013/09/17 14:20 nikolaj 2013/09/17 13:42 nikolaj 2013/09/17 13:39 nikolaj 2013/09/17 13:39 nikolaj 2013/09/17 13:38 nikolaj old revision restored (2013/09/17 13:33)2013/09/17 13:34 nikolaj 2013/09/17 13:33 nikolaj 2013/09/17 13:33 nikolaj old revision restored (2013/09/17 09:34) Next revision Previous revision 2013/09/17 14:32 nikolaj 2013/09/17 14:32 nikolaj 2013/09/17 14:31 nikolaj 2013/09/17 14:30 nikolaj 2013/09/17 14:28 nikolaj 2013/09/17 14:20 nikolaj 2013/09/17 13:42 nikolaj 2013/09/17 13:39 nikolaj 2013/09/17 13:39 nikolaj 2013/09/17 13:38 nikolaj old revision restored (2013/09/17 13:33)2013/09/17 13:34 nikolaj 2013/09/17 13:33 nikolaj 2013/09/17 13:33 nikolaj old revision restored (2013/09/17 09:34) Line 1: Line 1: ===== Fokker-Planck equation ===== ===== Fokker-Planck equation ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $n\in\mathbb N$ | + | @#55CCEE: context ​    | @#55CCEE: $n\in\mathbb N$ | - | @#88DDEE: $\mu:​C(\mathbb R^n,\mathbb R^n)$ | + | @#55CCEE: context ​    | @#55CCEE: $\mu:​C(\mathbb R^n,\mathbb R^n)$ | - | @#88DDEE: $D:​C^2(\mathbb R^n,\mathbb R^{n^2})$ | + | @#55CCEE: context ​    | @#55CCEE: $\mathsf{D}:​C^2(\mathbb R^n,\mathbb R^{n^2})$ | - | @#DDDDDD: $::​\mu(\mathbf{x})$ | + | @#DDDDDD: range       | @#DDDDDD: $::​\mu(\mathbf{x})$ | - | @#DDDDDD: $::​\mathsf{D}(\mathbf{x})$ | + | @#DDDDDD: range       | @#DDDDDD: $::​\mathsf{D}(\mathbf{x})$ | - | @#FFBB00: $f \in \mathrm{it}$ | + | @#FFBB00: definiendum ​| @#FFBB00: $f \in \mathrm{it}$ | - | @#55EE55: $f:​C^2(\mathbb R^n\times\mathbb R,\mathbb R)$  | + | @#55EE55: postulate ​  | @#55EE55: $f:​C^2(\mathbb R^n\times\mathbb R,\mathbb R)$  | - | @#DDDDDD: $::​f(\mathbf{x},​t) ​$ | + | @#DDDDDD: range       | @#DDDDDD: $::​f(\mathbf{x},​t) ​$ | - | @#55EE55: $\frac{\partial }{\partial t} f = -\mathrm{div} (\mu \cdot f) + \sum_{i=1}^{n} \sum_{j=1}^{n} \frac{\partial^2}{\partial x_i \, \partial x_j} (\mathsf{D}_{ij}\cdot f)$ | + | @#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 ==== ==== Discussion ====