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   Brownian Motion
   















 

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Brownian Motion

A variable subject to geometric Brownian motion has a lognormal probability distribution and will always have a positive mean. A variable with arithmetic Brownian motion will have a normal distribution. Arithmetic Brownian motion is also the name given to the irregular movement of pollen grains suspended in water. The phenomenon allegedly was observed by a botanist, Robert Brown, in 1828. This prototypical random movement was attributed to the effect of water molecules striking the pollen and dispersing it throughout the water. Although more recent work has suggested that Brown's optical equipment was not up to the observations he reported, the hypothesized random process is still the basis of many security price models. Also called Wiener or Wiener/Bachelier Process, Brownian motion is a type of Markov process. Also called Diffusion Process, Markov Process. See Lognormal Distribution, Martingale, Stochastic Process. See also Ito's Lemma.

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