On parameter estimation of fractional Ornstein–Uhlenbeck process

Abstract

Abstract We consider a problem of parameter estimation for the fractional Ornstein–Uhlenbeck model given by the stochastic differential equation d ⁢ X t = - θ ⁢ X t ⁢ d ⁢ t + d ⁢ B t H {dX_{t}=-\theta X_{t}dt+dB_{t}^{H}} , t ≥ 0 {t\geq 0} , where θ > 0 {\theta>0} is an unknown parameter to be estimated and B H {B^{H}} is a fractional Brownian motion with Hurst parameter H ∈ ( 0 , 1 ) {H\in(0,1)} . We provide an estimator for θ, and then we study its strong consistency and asymptotic normality. The main tool in our proofs is the paper [I. Nourdin, D. Nualart and G. Peccati, The Breuer–Major theorem in total variation: Improved rates under minimal regularity, Stochastic Process. Appl. 131 2021, 1–20].