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 their knowledge of the Stanford team's offense on the Brown team and turned B-Mo into a successful squad. While certainly not dominating the Northeast, Brown became a regional contender, returning to Regionals for the second year in a row. Brownian Motion had become a Northeastern power by this point and won a considerable number of the games it played. The 1986 and 1987 seasons saw a reasonably competitive team face some of the toughest teams in the country. The 1985-1986 season also saw beginnings of the "Fish" logo that remains the official symbol of Brownian Motion to this day, still