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
A computer-simulated realization of a Wiener or Brownian motion process on the surface of a sphere. The Wiener process is widely considered the most studied and central stochastic process in probability theory.
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.
Brownian motion
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Brownian motion is the random motion of particles suspended in a medium. The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often itself called "Browni
Perrin examined the equilibrium (barometric distribution) of granules (0.6 microns) of gamboge, a viscous substance, under the microscope. The granules move against gravity to regions of lower concentration. The relative change in density observed in 10 microns of suspension is equivalent to that occurring in 6 km of air.