Non-Gaussian statistics of anomalous diffusion: The DNA sequences of prokaryotes

We adopt a non-Gaussian indicator to measure the deviation from Gaussian statistics of a diffusion process generated by dichotomous fluctuations with infinite memory. We also make analytical predictions on the transient behavior of the non-Gaussian indicator as well as on its stationary value. We then apply this non-Gaussian analysis to the DNA sequences of prokaryotes adopting a theoretical model where the "DNA dynamics" are assumed to be determined by the statistical superposition of two independent generators of fluctuations: a generator of fluctuations with no correlation and a generator of fluctuations with infinite correlation "time." We study also the influence that the finite length of the observed sequences has on the non-Gaussian statistics of diffusion. We find that these non-Gaussian effects are blurred by the joint action of short-range fluctuation and sequence truncation. Nevertheless, under proper conditions, fulfilled by all the DNA sequences of prokaryotes that have been examined, a non-Gaussian signature remains to signal the correlated nature of the driving process.