  Herein we develop a dynamical foundation for fractional Brownian Motion. A
clear relation is established between the asymptotic behaviour of the
correlation function and diffusion in a dynamical system. Then, assuming that
scaling is applicable, we establish a connection between diffusion (either
standard or anomalous) and the dynamical indicator known as the Hurst
coefficient. We argue on the basis of numerical simulations that although we
have been able to prove scaling only for "Gaussian" processes, our conclusions
may well apply to a wider class of systems. On the other hand systems exist for
which scaling might not hold, so we speculate on the possible consequence on
the various relations derived in the paper on such systems.
