Pi (letter): Difference between revisions
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A simple mathematical representation of [[Brownian motion]], the '''Wiener equation''', named after [[Norbert Wiener]], 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. | |||
{{noreferences|date=January 2012}} | |||
[[Category:Stochastic differential equations]] | |||
{{probability-stub}} | |||
Revision as of 12:58, 23 November 2013
A simple mathematical representation of Brownian motion, the Wiener equation, named after Norbert Wiener, assumes the current velocity of a fluid particle fluctuates randomly:
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.