Brownian motion was identified by Robert Brown in 1827 after looking at the jittery movement of pollen on water. It can be defined as the apparent random motion of particles suspended on a fluid. The term is often associated with the 'random walk' phenomenon.
Brownian motion, and the mathematical models that describe it, have been used for over a century to describe a multitude of phenomena. For example, Einstein used Brownian motion to describe both the existence of atoms, and the kinetic model of thermal equilibrium. Among other things, economists have been using Brownian motion since the early 20th century to model the stock market. For a study of the diffusion of brownian spheres, see Hydrodynamic Coupling of two brownian spheres to a planar survace.
1. Einstein, A. "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat", Annalen der Physik, 17, 1905, 549-560