Fractional Brownian Motion

For any number H in the range 0 < H < 1, index H fractional Brownian motion is a random process Y(t) having increments Y(t + h) - Y(t) that are normally distributed with mean = 0 and standard deviation = hH.
Self-affinity is built in to fBm:
Prob(Y(t + h) - Y(t) < u) = Prob(Y(s⋅(t + h)) - Y(s⋅t) < sH⋅u)
Note that H = 1/2 fBm is just standard Brownian motion.

Return to fractional Brownian motion.