Wiener Process

Abstract

Brownian motion is the most renowned, and historically the first stochastic process that was thoroughly investigated. It is named after the English botanist, Robert Brown, who in 1827 observed that small particles immersed in a liquid exhibited ceaseless irregular motion. Brown himself mentions several precursors starting at the beginning with Leeuwenhoek (1632–1723). In 1905 Einstein, unaware of the existence of earlier investigations about Brownian motion, obtained a mathematical derivation of this process from the laws of physics. The theory of Brownian motion was further developed by several distinguished mathematical physicists until Norbert Wiener gave it a rigorous mathematical formulation in his 1918 dissertation and in later papers. This is why the Brownian motion is also called the Wiener process. For a brief history of the scientific developments of the process see Nelson (Dynamical theories of Brownian motion. Princeton: Princeton University Press, 1967).