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X is a Brownian motion with respect to P, i.e., the law of X with respect to P is the same as the law of an n-dimensional Brownian motion, i.e., the push-forward measure X ∗ (P) is classical Wiener measure on C 0 ([0, ∞); R n). both X is a martingale with respect to P (and its own natural filtration); and
Robert Brown was born in Montrose, Scotland on 21 December 1773, in a house that existed on the site where Montrose Library currently stands. He was the son of James Brown, a minister in the Scottish Episcopal Church with Jacobite convictions so strong that in 1788 he defied his church's decision to give allegiance to George III.
In mathematics, 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 discovered by Norbert Wiener. [1] [2] It is one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments).
In 1827, botanist Robert Brown used a microscope to look at dust grains floating in water. He found that the floating grains were moving about erratically; a phenomenon that became known as "Brownian motion". This was thought to be caused by water molecules knocking the grains about.
Robert Brown (botanist, born 1773) (1773–1858), Scottish (Montrose) scientist, explorer, author, botanist: R.Br., after whom Brownian motion is named Robert Brown (New Zealand botanist) (c. 1824–1906), New Zealand bootmaker and botanist: R.Br.bis
Drag dissipates kinetic energy, turning it into heat. The corresponding fluctuation is Brownian motion. An object in a fluid does not sit still, but rather moves around with a small and rapidly-changing velocity, as molecules in the fluid bump into it. Brownian motion converts heat energy into kinetic energy—the reverse of drag.
The term "Brownian motor" was originally invented by Swiss theoretical physicist Peter Hänggi in 1995. [3] The Brownian motor, like the phenomenon of Brownian motion that underpinned its underlying theory, was also named after 19th century Scottish botanist Robert Brown, who, while looking through a microscope at pollen of the plant Clarkia pulchella immersed in water, famously described the ...
Clarkia pulchella is most famous for its use by botanist Robert Brown in the discovery of Brownian motion. Brown studied the pollen of Clarkia pulchella while immersed in water under the microscope. He used these pollen granules because they contain oblong particles, which he observed were 6 to 8 micrometres in length, and he thought that he ...