Fractional Brownian motion with random Hurst exponent
- 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 cannot be attributed to a class of self-similar random processes. Inspired by these observations, we here study the process that preserves the properties of the 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 the fractional Brownian motion with the random Hurst exponent. The explicit formulas for probability density function, mean-squared displacement,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 cannot be attributed to a class of self-similar random processes. Inspired by these observations, we here study the process that preserves the properties of the 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 the fractional Brownian motion with the random Hurst exponent. The explicit formulas for probability density function, mean-squared 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.…
Author details: | Michal BalcerekORCiD, Krzysztof BurneckiORCiD, Samudrajit Thapa, Agnieszka WylomanskaORCiD, Aleksei ChechkinORCiDGND |
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DOI: | https://doi.org/10.1063/5.0101913 |
ISSN: | 1054-1500 |
ISSN: | 1089-7682 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/36182362 |
Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
Subtitle (English): | accelerating diffusion and persistence transitions |
Publisher: | AIP Publishing |
Place of publishing: | Melville |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/09/13 |
Publication year: | 2022 |
Release date: | 2024/09/20 |
Volume: | 32 |
Issue: | 9 |
Article number: | 093114 |
Number of pages: | 15 |
Funding institution: | Beethoven Grant [DFG-NCN 2016/23/G/ST1/04083]; Pikovsky-Valazzi matching; scholarship, Tel Aviv University; Sackler postdoctoral fellowship;; National Center of Science under Opus Grant [2020/37/B/HS4/00120];; Polish National Agency for Academic Exchange (NAWA) |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
License (German): | Keine öffentliche Lizenz: Unter Urheberrechtsschutz |
External remark: | Erratum: https://doi.org/10.1063/5.0210418 |