Markov Processes , Hurst Exponents , and Nonlinear Diffusion Equations with application to finance

@inproceedings{Bassler2015MarkovP,
  title={Markov Processes , Hurst Exponents , and Nonlinear Diffusion Equations with application to finance},
  author={Kevin E. Bassler and Gemunu H. Gunaratne and Lemaire Joseph and McCauley},
  year={2015}
}
We show by explicit closed form calculations that a Hurst exponent H≠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≠1/2. Thus Markov processes, which by construction have no long time correlations, can have H≠1/2. If a Markov process scales with Hurst exponent H≠1/2 then it simply means that the process has nonstationary increments. For the… CONTINUE READING