title: Memory effects in fractional Brownian motion with Hurst exponent H<1/3.
abstract: We study the regression to the origin of a walker driven by dynamically generated fractional Brownian motion (FBM) and we prove that when the FBM scaling, i.e., the Hurst exponent H<1/3 , the emerging inverse power law is characterized by a power index that is a compelling signature of the infinitely extended memory of the system. Strong memory effects leads to the relation H=θ/2 between the Hurst exponent and the persistent exponent θ , which is different from the widely used relation H=1-θ . The latter is valid for 1/3<H<1 and is known to be compatible with the renewal assumption.
authors.affiliation: Instituto de Alta Investigación, Universidad de Tarapacá, Chile.
authors.forename: Mauro
authors.initials: M
authors.lastname: Bologna
authors.forename: Fabio
authors.initials: F
authors.lastname: Vanni
authors.forename: Arkadii
authors.initials: A
authors.lastname: Krokhin
authors.forename: Paolo
authors.initials: P
authors.lastname: Grigolini