  There is much confusion in the literature over Hurst exponents. Recently, we
took a step in the direction of eliminating some of the confusion. One purpose
of this paper is to illustrate the difference between fBm on the one hand and
Gaussian Markov processes where H not equal to 1/2 on the other. The difference
lies in the increments, which are stationary and correlated in one case and
nonstationary and uncorrelated in the other. The two- and one-point densities
of fBm are constructed explicitly. The two-point density doesn't scale. The
one-point density is identical with that for a Markov process with H not 1/2.
We conclude that both Hurst exponents and histograms for one point densities
are inadequate for deducing an underlying stochastic dynamical system from
empirical data.
