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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 [[#References|[1]]]. 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.
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[[Category:Markov processes]]
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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.
  
 
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<table><TR><TD valign="top">[1]</TD> <TD valign="top">  V.P. Pavlov,   "Brownian motion" , ''Large Soviet Encyclopaedia'' , '''4''' (In Russian)</TD></TR></table>
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|valign="top"|{{Ref|P}}|| V.P. Pavlov, "Brownian motion" , ''Large Soviet Encyclopaedia'' , '''4''' (In Russian)
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  K. Itô,   H.P. McKean jr.,   "Diffusion processes and their sample paths" , Springer (1974) pp. Chapt. 1; 2</TD></TR></table>
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|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}}
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Latest revision as of 06:24, 11 May 2012

2020 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.

References

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

Comments

See also Wiener measure.

References

[IM] K. Itô, H.P. McKean, "Diffusion processes and their sample paths" , Springer (1974) pp. Chapt. 1; 2 MR0345224 Zbl 0285.60063
How to Cite This Entry:
Brownian motion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Brownian_motion&oldid=16455
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