Brownian Motion

Brownian motion is the random movement of particles suspended in a fluid, caused by their collisions with the fast moving molecules of the fluid, and also the name of the mathematical model, also called the Wiener process, used to describe such movement and a wide class of related random processes. The physical phenomenon is named after the botanist Robert Brown, who observed the erratic motion of pollen grains suspended in water in 1827, though the motion itself had been noted earlier and its full physical explanation, in terms of molecular collisions, was given by Albert Einstein in 1905. As a mathematical object, Brownian motion is a continuous time stochastic process with independent, normally distributed increments, and it forms the basis of stochastic calculus, with applications ranging from statistical mechanics to the mathematical modeling of financial markets.