Mathematically, a Brownian motion process is such that if we know a particle's position is p at time 0, then the particle's position at subsequent time t is a normally distributed random variable with a mean of p and a variance of t. Brownian motion is a kind of [stochastic process]?.

The mathematical theory of Brownian motion has been applied in contexts ranging far beyond the movement of particles in fluids. For example, in the modern theory of [option pricing]?, asset classes are sometimes modelled as if they move according to a Brownian motion with drift.

See also diffusion, and osmosis.