title: Fractional brownian motion run with a nonlinear clock.
abstract: 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.
authors.affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47097, USA. omalled@math.purdue.edu
authors.forename: Daniel
authors.initials: D
authors.lastname: O'Malley
authors.forename: John H
authors.initials: JH
authors.lastname: Cushman