Brownian motion

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2010 Mathematics Subject Classification: Primary: 60J65 [MSN][ZBL]

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 [P]. The model of Brownian motion which is the most important one in the theory of random processes is the so-called Wiener process, and the concept of Brownian motion is in fact often identified with this model.


[P] V.P. Pavlov, "Brownian motion" , Large Soviet Encyclopaedia , 4 (In Russian)


See also Wiener measure.


[IM] K. Itô, H.P. McKean, "Diffusion processes and their sample paths" , Springer (1974) pp. Chapt. 1; 2 MR0345224 Zbl 0285.60063
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