Brownian motion linear and angular momenta remain null over time. It is important also to note that the kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations sum up to the caloric component of a fluid's internal energy. This motion is named after the botanist Robert Brown, who was the most eminent microscopist of his time. In 1827, while looking through a microscope at pollen of the plant "Clarkia pulchella" immersed in water, the triangular shaped pollen burst at the corners, emitting particles which he noted jiggled around in the water in random fashion. He was
Brownian model of financial markets for buying or selling). Another assumption is that asset prices have no jumps, that is there are no surprises in the market. This last assumption is removed in jump diffusion models. Consider a financial market consisting of formula_1 financial assets, where one of these assets, called a "bond" or "money market", is risk free while the remaining formula_2 assets, called "stocks", are risky. A "financial market" is defined as formula_3 that satisfies the following: Let formula_17 be a probability space, and a formula_18 be D-dimensional Brownian motion stochastic process, with the natural filtration: If formula_20 are the measure 0 (i.e.