I need help understanding the Mandelbot and Van Ness' definition of Fractional Brownian motion

$ B_H( t , \omega ) - B_H( 0 , \omega ) = \frac{1}{\Gamma(H + \frac{1}{2})} ( \int_{-\infty}^0 [(t - s)^{H - \frac{1}{2}} - (-s)^{H - \frac{1}{2}}t] dB(s, \omega) + \int_0^t (t - s)^{H - \frac{1}{2}} dB(s, \omega) ) $

(from "Fractional Brownian Motions, Fractional Noises and Applications" by Mandelbrot and Van Ness, 1968).

All I've been able to find out is that the above equation is the moving average of past white noise but I don't understand how it is so, and the motivation for the various terms.


I think you should have a look at this




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