Wiener process
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In mathematics, the Wiener process is a real-valued continuous-time stochastic process named after Norbert Wiener. It is one of the best known Lévy processes. It occurs frequently in pure and applied
The generator of Brownian motion on Riemannian manifolds is 1⁄2 times the Laplace–Beltrami operator. The image above shows Brownian motion on the surface of a 2-sphere.
Stochastic process
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In probability theory and related fields a stochastic or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family o
Wiener process
…the Wiener process (or Brownian motion, due to its historical connection with the physical process of the same name) is a real-valued continuous-time stochastic process named after Norbert Wiener. It is one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments). It occurs…
Mathematician Joseph Doob did early work on the theory of stochastic processes, making fundamental contributions, particularly in the theory of martingales. His book Stochastic Processes is considered highly influential in the field of probability theory.
Norbert Wiener gave the first mathematical proof of the existence of the Wiener process. This mathematical object had appeared previously in the work of Thorvald Thiele, Louis Bachelier, and Albert Einstein.