Editing Wiener equation

{{short description|Mathematical representation of Brownian motion}}
{{More citations needed|date=February 2021}}
A simple mathematical representation of [[Brownian motion]], the '''Wiener equation''', named after [[Norbert Wiener]],<ref name="Masani2012">{{cite book|author=Pesi R. Masani|title=Norbert Wiener 1894–1964|url=https://books.google.com/books?id=anD0BwAAQBAJ&pg=PA134|date=6 December 2012|publisher=Birkhäuser|isbn=978-3-0348-9252-0|pages=134–}}</ref> assumes the current [[velocity]] of a [[fluid]] particle fluctuates [[random]]ly:

:<math>\mathbf{v} = \frac{d\mathbf{x}}{dt} = g(t),</math>

where '''v''' is [[velocity]], '''x''' is position, ''d/dt'' is the time [[derivative]], and ''g(t)'' may for instance be [[white noise]].

Since velocity changes instantly in this formalism, the ''Wiener equation'' is not suitable for short time scales.  In those cases, the [[Langevin equation]], which looks at particle [[acceleration]], must be used.

==References==
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[[Category:Stochastic differential equations]]


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