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.
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