Question: Communication Mandelbrot

When Benoit Mandelbrot was still alive I sent him an email:

Hi,
I am writing to you because I have trouble understanding why
the covariance function in the Fractional Brownian Motion (FBM) is given by:

(t[i]^(2*H)+t[j]^(2*H)-abs(t[i]-t[j])^(2*H))/2)

I would be very grateful if you could please explain this to me in simple and step by step terms.
I understand simple ARIMA models (P(t)=P(t-1)+E(t) where E(t)=p*E(t-1)+r(t)) which have the
same serial correlated properties as the Fractional Brownian Motion but I guess the notation is
different in the FBM due to the Hurst exponent.

The reply I got was:

Your questions are likely to be answered by the extensive notes at the end of the book The Misbehavior of markets,  by Mandelbrot and Hudson.AKM

Unfortunatly, to this day I have not been able to get a hold of such a book.

My question still remains unanswered:

Why is the covariance function in the Fractional Brownian Motion (FBM):

(t[i]^(2*H)+t[j]^(2*H)-abs(t[i]-t[j])^(2*H))/2) ??

For a 3 time periods the covariance matrix is given by:

restart; Matrix(3, proc (i, j) options operator, arrow; (1/2)*t[i]^(2*H)+(1/2)*t[j]^(2*H)-(1/2)*abs(t[i]-t[j])^(2*H) end proc);

A := eval(Matrix(3, proc (i, j) options operator, arrow; (1/2)*t[i]^(2*H)+(1/2)*t[j]^(2*H)-(1/2)*abs(t[i]-t[j])^(2*H) end proc), {H = 0, t[1] = 1, t[2] = 2, t[3] = 3})


If the Hurst Exponent
                                   H = 0.5
 then the increments of the process are serial independent (Brownian Motion, Pure Random Walk)

If the Hurst Exponent
                                  >(H, 0.5)
 then the increments of the process are positively serial dependent

If the Hurst Exponent
                                   H < 0.5
 then the increments of the process are negatively serial dependent