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The various linear fractional Lévy motions

Gennady Samorodnitsky
Murad S. Taqqu

Abstract:

We treat in this paper a problem raised by Cambanis and Maejima (1988). Linear Fractional Lévy motions are -stable self-similar processes with stationary increments and a ``moving average'' representation. The representation involves two real parameters a and b. When , the processes are identical to the Gaussian Fractional Brownian motion for all values of a and b. We will show that different values of the parameters a and b yield different processes when and when the skewness intensity is not necessarily zero.