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arXiv · 1301.7638

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

Denis Boyer·David S. Dean·Carlos Mejia-Monasterio·Gleb Oshanin
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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 $H\simeq0.30$, a value in the subdiffusive regime.

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Denis Boyer, David S. Dean, Carlos Mejia-Monasterio, Gleb Oshanin. 2013-01-31. On ergodic least-squares estimators of the generalized diffusion coefficient for fractional Brownian motion. https://doi.org/10.1103/physreve.87.030103

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