NON-GAUSSIAN STATISTICS OF ANOMALOUS DIFFUSION - THE DNA-SEQUENCES OFPROKARYOTES

We adopt a non-Gaussian indicator to measure the deviation from Gaussi an statistics of a diffusion process generated by dichotomous fluctuat ions with infinite memory. We also make analytical predictions on the transient behavior of the non-Gaussian indicator as well as on its sta tionary value. We then apply this non-Gaussian analysis to the DNA seq uences of prokaryotes adopting a theoretical model where the ''DNA dyn amics'' are assumed to be determined by the statistical superposition of two independent generators of fluctuations: a generator of fluctuat ions with no correlation and a generator of fluctuations with infinite correlation ''time.'' We study also the influence that the finite len gth of the observed sequences has on the non-Gaussian statistics of di ffusion. We find that these non-Gaussian effects are blurred by the jo int action of short-range fluctuation and sequence truncation. Neverth eless, 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.