Fractional Brownian motion stationary and self-similar increments. It has stationary increments: For "H" > ½ the process exhibits long-range dependence, Sample-paths are almost nowhere differentiable. However, almost-all trajectories are locally Hölder continuous of any order strictly less than "H": for each such trajectory, for every "T" > 0 and for every "ε" > 0 there exists a (random) constant "c" such that for 0 < "s","t" < "T". With probability 1, the graph of "B"("t") has both Hausdorff dimension and box dimension of 2−"H". As for regular Brownian motion, one can define stochastic integrals with respect to fractional Brownian motion, usually called "fractional
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