Brownian bridge of the Brownian bridge based on the Brownian motion is, for "t" ∈ [0, T] Conversely, for "t" ∈ [0, ∞] The Brownian bridge may also be represented as a Fourier series with stochastic coefficients, as where formula_9 are independent identically distributed standard normal random variables (see the Karhunen–Loève theorem). A Brownian bridge is the result of Donsker's theorem in the area of empirical processes. It is also used in the Kolmogorov–Smirnov test in the area of statistical inference. A standard Wiener process satisfies "W"(0) = 0 and is therefore "tied down" to the origin, but other points are not
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