Brownian motion (named after Robert Brown, who first observed the motion in 1827, when he examined pollen grains in water), or pedesis (from Greek: πήδησις "leaping") is the assumably random movement of particles suspended in a fluid (i.e., a liquid such as water or a gas such as air) or the mathematical model used to describe such random movements, often called a particle theory.
The mathematical model of Brownian motion has several real-world applications. An often quoted example is stock market fluctuations. However, movements in share prices may arise due to unforeseen events which do not repeat themselves.
Brownian motion is among the simplest of the continuous-time stochastic (or probabilistic) processes, and it is a limit of both simpler and more complicated stochastic processes (see random walk and Donsker's theorem). This universality is closely related to the universality of the normal distribution. In both cases, it is often mathematical convenience rather than the accuracy of the models that motivates their use. This is because Brownian motion, whose time derivative is everywhere infinite, is an idealized approximation to actual random physical processes, which always have a finite time scale.