Wiener process [SEP] named after
Wiener process
In mathematics, the Wiener process is a continuous-time stochastic process named in honor of American mathematician Norbert Wiener. It is often called standard Brownian motion process or 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.
The Wiener process
Itô isometry
In mathematics, the Itô isometry, named after Kiyoshi Itô, is a crucial fact about Itô stochastic integrals. One of its main applications is to enable the computation of variances for random variables that are given as Itô integrals.
Let formula_1 denote the canonical real-valued Wiener process defined up to time formula_2, and let formula_3 be a stochastic process that is adapted to the natural filtration formula_4 of the Wiener process. Then
where formula_6 denotes expectation with respect to classical Wiener measure. 
In other words