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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...

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