Difference between revisions of "Brownian motion"
From Encyclopedia of Mathematics
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| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> | + | <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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| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> | + | <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 {{MR|0345224}} {{ZBL|0285.60063}} </TD></TR></table> |
Revision as of 10:30, 27 March 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 [1]. 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
| [1] | V.P. Pavlov, "Brownian motion" , Large Soviet Encyclopaedia , 4 (In Russian) |
Comments
See also Wiener measure.
References
| [a1] | K. Itô, H.P. McKean jr., "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=23590
Brownian motion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Brownian_motion&oldid=23590