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We consider the Langevin equation which contains an unknown drift parameter θ and where the noise is modeled as fractional Brownian motion with Hurst index H ∈ (0, 1 2 ). The solution corresponds to the fractional Ornstein-Uhlenbeck process. We construct an estimator, based on discrete observations in time, of the unknown drift parameter, that is similar in form to the maximum likelihood estimator for the drift parameter in Langevin equation with standard Brownian motion. It is assumed that thedoi:10.1214/15-ejs1062 fatcat:cks5io7jofhwhi5ln7g2xh33he