Fractional brownian motion run with a nonlinear clock.

We construct a family of stochastic processes with nonstationary, correlated increments which allow a priori independent selections of both fractal dimension and mean-square displacement. The family is essentially fractional Brownian motion (fBm) run with a nonlinear clock (fBm-nlc). The fractal dimension of fBm-nlc is shown to be the same as that of the underlying fBm process. We also compute the p-variation and discuss the problems in using this to differentiate between diffusive processes. The fBm-nlc process illustrates that the range of anomalous diffusive processes has not been adequately explored.