View source for Brownian motion

{{MSC|60J65}}

[[Category:Markov processes]]

The process of chaotic displacements of small particles suspended in a liquid or in a gas which is the result of collisions with the molecules of the medium. There exist several mathematical models of this motion {{Cite|P}}. The model of Brownian motion which is the most important one in the theory of random processes is the so-called [[Wiener process|Wiener process]], and the concept of Brownian motion is in fact often identified with this model.

====References====
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|valign="top"|{{Ref|P}}|| V.P. Pavlov, "Brownian motion" , ''Large Soviet Encyclopaedia'' , '''4''' (In Russian)
|}

====Comments====
See also [[Wiener measure|Wiener measure]].

====References====
{|
|valign="top"|{{Ref|IM}}|| K. Itô, H.P. McKean, "Diffusion processes and their sample paths" , Springer (1974) pp. Chapt. 1; 2 {{MR|0345224}} {{ZBL|0285.60063}}
|}