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 Ultimate squared off against defending champions Colorado. Colorado, led by 2004 Callahan Award winner Josh "Richter" Ackley and sophomore Beau Kittredge, had had a more successful spring season than Brown, but the two teams had not yet faced each other. The night before the game, Brown's Josh Ziperstein was announced the 2005 Callahan Award winner, leading to a rare occurrence of two Callahan Award winners playing against each other in the finals. Brown defeated Colorado 15-14 in a game that featured incredible plays by both Brown and Colorado. 2005 2004 2003 2002 2001 2000 1999 1998 1996 Brownian Motion Ultimate Brownian