fBm generalizes Brownian motion with long-range correlations. The Hurst exponent H controls roughness: H<0.5 = anti-persistent (rough), H=0.5 = Brownian, H>0.5 = persistent (smooth trends).
Spectral synthesis: Gaussian noise → 1/fH+0.5 power shaping → IFFT → cumulative sum
H=0.1: jagged anti-correlated | H=0.5: standard Brownian | H=0.9: smooth persistent trends