Expectation (mathematics) in the context of "Fractional Brownian motion"

In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process ${\textstyle B_{H}(t)}$ on ${\textstyle [0,T]}$, that starts at zero, has expectation zero for all ${\displaystyle t}$ in ${\textstyle [0,T]}$, and has the following covariance function:

where H is a real number in (0, 1), called the Hurst index or Hurst parameter associated with the fractional Brownian motion. The Hurst exponent describes the raggedness of the resultant motion, with a higher value leading to a smoother motion. It was introduced by Mandelbrot & van Ness (1968).