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 instead of the usual two. When Tufts soundly defeated Brown in the finals at regionals, Brown missed nationals for the first time since 1997. The bright spot for Brownian Motion was the extremely talented freshman class, including Alexander Bowman, Dan MacArthur, Neale Mahoney, Ben Sprung, Paul Vandenberg, and future Callahan Award winner Joshua "Zip" Ziperstein. Entering the 2003 season, Brown was looking to be one of the top programs in college Ultimate, despite failing to qualify for Nationals the previous year. With a relatively young team, Brown won regionals without losing a game, beating a talented UMass squad 17-15 in