= Fractional Brownian motion
{title2=$\mathbb E[B_H(s)B_H(t)]=\tfrac12(s^{2H}+t^{2H}-|s-t|^{2H})$}
{wiki}
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 $\sqrt2$; 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>.
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