in mathematics, the wiener process is a real valued continuous-time stochastic process named in honor of american mathematician norbert wiener for his investigations on the mathematical properties of the one-dimensional brownian motion. it is often also called brownian motion due to its historical connection with the physical process of the same name originally observed by scottish botanist robert brown. it is one of the best known lévy processes (càdlàg stochastic processes with stationary independent increments) and occurs frequently in pure and applied mathematics, economics, quantitative finance, evolutionary biology, and physics.