Brownian motion

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