Fractional Brownian motion

Summary

Fractional Brownian motion is a continuous centred Gaussian process with stationary increments that is self-similar with a Hurst index $H \in (0, 1)$. For $H = 1/2$ it is the Wiener process. For $H \ne 1/2$ its increments are correlated. For $H > 1/2$ this gives long memory, which is used to model data in hydrology, finance and network traffic.