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Memory effects in fractional Brownian motion with Hurst exponent H<1/3
Mauro Bologna1, Fabio Vanni, Arkadii Krokhin
1Instituto de Alta Investigación, Universidad de Tarapacá, Chile.
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
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