Fractional Brownian Motion

One way to simulate fBm is by randomizing a construction due to Weierstrass.

Given numbers b > 1 and 0 < H < 1, define a function w(t) by

w(t) = c1b-Hsin(b1t + d1) + c2b-2Hsin(b2t + d2) + c3b-3Hsin(b3t + d3) + ...

where the ci are normally distributed with mean 0 and standard deviation 1, and the di are uniformly distributed in the interval 0 ≤ di < 2⋅π.

We use this method to generate examples of fBm.

Return to fractional Brownian motion.