Brownian motion but rather a singular behavior in which the particle doesn't move at all. The Brownian motion can be modeled by a random walk. Random walks in porous media or fractals are anomalous. In the general case, Brownian motion is a non-Markov random process and described by stochastic integral equations. The French mathematician Paul Lévy proved the following theorem, which gives a necessary and sufficient condition for a continuous R-valued stochastic process "X" to actually be "n"-dimensional Brownian motion. Hence, Lévy's condition can actually be used as an alternative definition of Brownian motion. Let "X" = ("X", ..., "X") be a
Brownian motion mingling motion of dust particles is caused largely by air currents, the glittering, tumbling motion of small dust particles is, indeed, caused chiefly by true Brownian dynamics. While Jan Ingenhousz described the irregular motion of coal dust particles on the surface of alcohol in 1785, the discovery of this phenomenon is often credited to the botanist Robert Brown in 1827. Brown was studying pollen grains of the plant "Clarkia pulchella" suspended in water under a microscope when he observed minute particles, ejected by the pollen grains, executing a jittery motion. By repeating the experiment with particles of inorganic matter he