We show by explicit closed form calculations that a Hurst exponent H≠12 does not necessarily imply long time correlations like those found in fractional Brownian motion (fBm). We construct a large set of scaling solutions of Fokker–Planck partial differential equations (pdes) where H≠12....

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 fractional Brownian motion (fBm) on the one hand and Gaussian Markov processes where...

We discuss the deep connection between nonstationary increments, martingales, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). We explain why a test for a martingale is generally a test for uncorrelated increments. We explain why...