Estimation of the Hurst parameter from continuous noisy data

Pavel Chigansky, Marina Kleptsyna

Research output: Contribution to journalArticlepeer-review


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 3{4, 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.

Original languageAmerican English
Pages (from-to)2343-2385
Number of pages43
JournalElectronic Journal of Statistics
Issue number2
StatePublished - 2023

Bibliographical note

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© 2023, Institute of Mathematical Statistics. All rights reserved.


  • Fractional Brownian motion
  • Hurst parameter estimation
  • Local Asymptotic Normality


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