2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144297We estimate the Hurst parameter $H$ of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of $H$ more difficult since relevant information is mostly contained in the high frequencies of the signal. We quantify the difficulty of the statistical problem in a min-max sense: we prove that the rate $n^{-1/(4H+2)}$ is optimal for estimating $H$ and propose rate optimal estimators based on adaptive estimation of quadratic functionals.Published in at http://dx.doi.org/10.1214/009053607000000316 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory60G18, 62G99, 62F12, 62M09text