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. |