Friday, February 1, 2013

1301.7638 (Denis Boyer et al.)

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

Denis Boyer, David S. Dean, Carlos Mejia-Monasterio, Gleb Oshanin
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.
View original: http://arxiv.org/abs/1301.7638

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