This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. When the Hurst parameter is greater than , consistent estimation is possible only if either the length of the observation interval increases to infinity or intensity of the noise decreases to zero. The main result is a proof of the Local Asymptotic Normality (LAN) of the model in these two regimes which reveals the optimal minimax estimation rates.
Pavel Chigansky was supported by ISF 1383/18 grant. Marina Kleptsyna was supported by ANR EFFI grant.
"Estimation of the Hurst parameter from continuous noisy data." Electron. J. Statist. 17 (2) 2343 - 2385, 2023. https://doi.org/10.1214/23-EJS2156