Fractional Brownian motion with fluctuating diffusivities

Abstract

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.

arXiv comment11 pages, 3 figures

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Cited by in corpus (4)

• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Two-dimensional Brownian motion with dependent components: turning angle analysis
• Evaluating Gaussianity of heterogeneous fractional Brownian motion
• Improved mean squared displacement analysis for anomalous single particle trajectories