On ergodic least-squares estimators of the generalized diffusion coefficient for fractional Brownian motion

Abstract

We analyse a class of estimators of the generalized diffusion coefficient for fractional Brownian motion $B_t$ of known Hurst index $H$, based on weighted functionals of the single time square displacement. We show that for a certain choice of the weight function these functionals possess an ergodic property and thus provide the true, ensemble-averaged, generalized diffusion coefficient to any necessary precision from a single trajectory data, but at expense of a progressively higher experimental resolution. Convergence is fastest around $H\simeq 0.30$, a value in the subdiffusive regime.

4 pages and 2 figures

References in corpus (3)

• Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
• Time-averaged MSD of Brownian motion
• Optimal fits of diffusion constants from single time data points of Brownian trajectories

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