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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.
Pacheco-Pozo et al. (Mon,) studied this question.