Fractional Brownian motion with random Hurst exponent: accelerating diffusion and persistence transitions

Abstract

Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The correlation and diffusion properties of this random motion are fully characterized by its index of self-similarity, or the Hurst exponent. However, recent single particle tracking experiments in biological cells revealed highly complicated anomalous diffusion phenomena that can not be attributed to a class of self-similar random processes. Inspired by these observations, we here study the process which preserves the properties of fractional Brownian motion at a single trajectory level, however, the Hurst index randomly changes from trajectory to trajectory. We provide a general mathematical framework for analytical, numerical and statistical analysis of fractional Brownian motion with random Hurst exponent. The explicit formulas for probability density function, mean square displacement and autocovariance function of the increments are presented for three generic distributions of the Hurst exponent, namely two-point, uniform and beta distributions. The important features of the process studied here are accelerating diffusion and persistence transition which we demonstrate analytically and numerically.

arXiv comment16 pages, 10 figures

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Cited by in corpus (9)

• Quantitative evaluation of methods to analyze motion changes in single-particle experiments
• Modelling intermittent anomalous diffusion with switching fractional Brownian motion
• Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches
• Fractional Brownian motion with fluctuating diffusivities
• Multifractional Brownian motion with telegraphic, stochastically varying exponent
• Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift
• Super-resolved anomalous diffusion: deciphering the joint distribution of anomalous exponent and diffusion coefficient
• Evaluating Gaussianity of heterogeneous fractional Brownian motion
• Improved mean squared displacement analysis for anomalous single particle trajectories