  We show by explicit closed form calculations that a Hurst exponent H that is
not 1/2 does not necessarily imply long time correlations like those found in
fractional Brownian motion. We construct a large set of scaling solutions of
Fokker-Planck partial differential equations where H is not 1/2. Thus Markov
processes, which by construction have no long time correlations, can have H not
equal to 1/2. If a Markov process scales with Hurst exponent H then it simply
means that the process has nonstationary increments. For the scaling solutions,
we show how to reduce the calculation of the probability density to a single
integration once the diffusion coefficient D(x,t) is specified. As an example,
we generate a class of student-t-like densities from the class of quadratic
diffusion coefficients. Notably, the Tsallis density is one member of that
large class. The Tsallis density is usually thought to result from a nonlinear
diffusion equation, but instead we explicitly show that it follows from a
Markov process generated by a linear Fokker-Planck equation, and therefore from
a corresponding Langevin equation. Having a Tsallis density with H not equal to
1/2 therefore does not imply dynamics with correlated signals, e.g., like those
of fractional Brownian motion. A short review of the requirements for
fractional Brownian motion is given for clarity, and we explain why the usual
simple argument that H unequal to 1/2 implies correlations fails for Markov
processes with scaling solutions. Finally, we discuss the question of scaling
of the full Green function g(x,t;x',t') of the Fokker-Planck pde.
