 Fractional Brownian motion

A fractional Brownian motion with Hurst exponent $H\in (0,1)$ is a centered Gaussian process with the displayed standard covariance function and a continuous modification. Its increment variance is $|s-t{|}^{2H}$. Some sources omit the factor $1/2$, multiplying the process by $\sqrt{2}$; the corresponding increment variance is then $2|s-t{|}^{2H}$. Its canonical pseudometric of a Gaussian process is proportional to $|s-t{|}^H$, which gives finite expected value of its absolute supremum on compact intervals through the Dudley entropy integral.