ما معنى Fractional Brownian motion؟

Fractional Brownian motion with Hurst exponent $H \in (0, 1)$ is the centred Gaussian process with $B_H(0) = 0$ and $\E[B_H(t)B_H(s)] = \frac12(t^{2H} + s^{2H} - |t - s|^{2H})$ (Mandelbrot and Van Ness, 1968). For $H = \frac12$ it is Brownian motion; for $H > \frac12$ its increments are positively correlated with power-law decay, for $H < \frac12$ negatively.