Brownian motion

The term Brownian motion (in honor of the botanist Robert Brown) refers to either

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• The physical phenomenon that minute particles immersed in a fluid move about randomly; or
• The mathematical models used to describe those random movements.

The mathematical model can also be used to describe many phenomena not resembling (other than mathematically) the random movement of minute particles. An often quoted example is stock market fluctuations. Another example is the evolution of physical characteristics in the fossil record.

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Brownian motion is among the simplest stochastic processes on a continuous domain, and it is a limit of both simpler (see random walk) and more complicated stochastic processes. This universality is closely related to the universality of the normal distribution. In both cases, it is often mathematical convenience rather than accuracy as models that motivates their use. All three quoted examples of Brownian motion are cases of this:

Related Topics:
Stochastic process - Limit - Random walk - Universality - Normal distribution

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• It has been argued that Lévy flights are a more accurate, if still imperfect, model of stock-market fluctuations.
• The physical Brownian motion can be modelled more accurately by a more general diffusion process.
• The dust hasn't settled yet on what the best model for the fossil record is, even after correcting for non-Gaussian data.
 
Brownian motion: History ►