Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach of a generalization that incorporates heterogeneities in either the tracers or the environment. This work presents a modification of Levy's representation of fBm for the case in which the generalized diffusion coefficient is a stochastic process. We derive analytical expressions for the autocovariance function and both ensemble- and time-averaged mean squared displacements. Further, we validate the efficacy of the developed framework in two-state systems, comparing analytical asymptotic expressions with numerical simulations.
@article{arxiv.2405.03836,
title = {Fractional Brownian motion with fluctuating diffusivities},
author = {Adrian Pacheco-Pozo and Diego Krapf},
journal= {arXiv preprint arXiv:2405.03836},
year = {2024}
}